1965 Valiant brake woes

Cobbled together or not, if the parts themselves are working correctly, and properly fitted; then anything works with anything. Brakes are not rocket science. How well they work together as a team, only depends on the "tune", which is the sizing of the various parts
Assuming the drum system is staying;
#1) ignore the rear brakes for now at best they are usually sized to not do more than 15% of the stopping

#2 Start by replacing the Booster Cuz clearly it is NOT working correctly. IMO the control valve inside it is busted, and there's only one way that happens, someone mashed the pedal with an improperly adjusted pushrod, and/or with excessive pedal-travel, for whatever reason; be-it hydraulic or mechanical.
It's a drum/drum system, this is as simple as it gets. Like I said, it ain't rocket science.

#3) Address the contact patch mismatch that is causing your pull.
The "pull" is caused by an imbalance in the L/R system. It could be Hydraulic, but more likely is mechanical. Drum brakes are self energizing, so the friction materials are the first suspects. With New linings, that have not been ground to match the drums, there is no controlling the contact patch, and if one side has more than the other, it will pull to that side, and there is nothing you can do about it. So fix this.
Furthermore; As long as the shoes are rubbing on their high points, the brake-drums are gonna flex with heavy application, causing a spongy feel, and lack of confidence, not to mention very poor ability to slow the car, at speed.
#4) with the shoes now working, revisit the pedal for being hard and high. If it it is not so, here is what I would do;
What I would do is remove ALL four drums and ALL the brake hardware, and ALL the rubber boots on ALL the w/c's. Then I would C-clamp across ALL the w/c pistons to keep them from coming out.
Then, I would again visit the pedal for high and hard. This is the only way, in your system, that you can ever know whether you have a hydraulic problem, or a mechanical problem, or some combination.
IF, your pedal is not high and hard now
;
Most likely there is air in the System, but this is not a sure thing; You could still have a mechanical issue between the pedal and the M/C. With a new booster in there, this pretty much points to the connecting links.
Solution is by process of elimination. First:
If you suspect air in the system, start by bench bleeding the master; yes, take it off and take it back to the bench-vise. Observe how it is designed, and where air can collect. Install the bleeder hoses, ends lowered into the fluid, and Full Stroke that beotch. If the fluid enters the transparent hoses from the lines, but returns back the way it came, this is NOT bleeding. The fluid has to go around the circle. from line out, up the line, and drop back into the reservoir. Sometimes you have to pinch the line, to prevent back-flow. When you think yur done, change the angle of the reservoir to nose up, cuz little bubble likes to remain in the nose, and between the two pistons inside the Power-chamber. Then reposition nose down, to get the last of it out the C-ports.
After you think you got it all, keep pumping, cuz micro-bubbles like to stick to things inside the chambers. If you don't get them out at this stage, eventually they are gonna make trouble.
After the M/C is re-installed, it is almost guaranteed that a small bubble will remain at the junction of the lines to the M/C. Purge it by cracking the connection, while a helper is gently pushing on the pedal. If that air goes back up into the master, it's gonna be trapped in the bore somewhere and with the M/C nose up, it's likely to stay in there forever.
Next, I gotta tell ya; If there is air in the system anywhere, it will act like an air spring. When you step on the pedal hard, you can easily generate 800 psi or more in the line. When you step off the pedal, that air will try to instantly go back to zero. In doing so, it will supercharge the fluid back to the M/C, and if the lid is off, you will see a geyser in the reservoir(s). Which could spurt two or three feet up towards the hood. and when it comes down, it will make a mess. and most non-silicone brake-fluids attack paint. You have been warned.
Wipe up spills with paper towels ASAP and wipe the area with a Brakleened paper-wipe.
You can mitigate this by coming off the pedal very slowly, and having a helper observe the geyser..
Now, if the C-clamped system is free of air;
the returning fluid will only roil in the bottom of the reservoir, and you may barely see it. The only amount of fluid that can return is the few or couple or maybe just one CC that went out, and it is returning thru the tiny Compensating port. If you see NO ROILING at all, chances are that your pushrod is too long, and the C-port is not passable. Shine a light into the reservoir looking for a shiney reflection coming at you from the port. If you see it, the pushrod is too long.
If the pushrod is too short, it will take a lot of pedal travel for the pushrod to actually reach the power piston, AND if your booster does not have the distance capacity, you might break the control valve trying to get there. So DO NOT power thru the long-travel. With a C-clamped system, engine not running, the pedal should be high and hard within one inch or less. This pushrod length is almost critical within too short or too long, so always adjust too long , to protect the booster, and work towards opening the C-port.
Ok so
once the geyser(s) are eliminated, the pedal should be hard.
Now you can prove the C-port is open by;
stab the pedal two or three times in rapid succession. This will prevent fluid backflow and the pedal should climb ever higher. Now release the pedal and wait a couple of seconds, for the fluid to return. Then step on the pedal, which should have normalized to as it was before the test.
If your pedal does not get higher, or does not normalize, most likely the fluid is not retuning and the usual suspect is a closed or restricted C-port. Shorten the rod not more than one turn atta time, and shine a light into the C-port. If you have a helper, slowly pumping the pedal back and forth, it will be easy to see the shiny reflection, which, you should NOT be seeing with the pedal parked!. As soon as the pedal works properly, it is short enough. It can be further shortened at a later time as a tuning trick; But all you need right now, is for it not to be too long.
#4A) This is a good time to check your booster (with the wc's still clamped. With your foot pressing moderately and holding, start the engine. As the booster charges, the pedal will drop. How far it drops will depend on how hard you are pressing. One inch or more is common with C-clamped w/c's. Later, with the brakes reassembled and adjusted with bedded-in shoes, you can expect pedal-drop of more than two inches, maybe closer to three, but still several inches off the floor. IF you do not have reserve room, then then if you ever have a failure and your foot drops on the brake-pedal during the event, it better not hit the floor!
#5) With the pedal now being high and hard, the C-port exhausting normally, and no geysers, the hydraulics are finally trustworthy. So now you can remove the C-clamps, reinstall the mechanical system, adjust it, and roadtest it.
#6) as for the mechanical system. By now, you should be intimately familiar with the mechanical system, so I'll only mention these three things;
1) If you have a parking brake, make sure the strut inside the drum, that interconnects the two shoes, is not preventing any shoe from parking on it's anchor. If it interferes then you may have a spongy pedal and lousy stopping
2) each drum should have one long friction shoe, and one short one. The long one goes to the rear of the car, so that they both wear at about the same rate.
3) the bane of any mechanical brake system, is flex. Look for it and try to eliminate it. Besides old hoses, unbedded shoes, and the aforementioned parking strut, about the only other source that I can think of is front wheel-bearing adjustment, and/or worn-out rear wheel-bearings. If the drums cannot stay centered, you will have issues.

I know it's a lotta work, but when you get it done, step by step, it will work, and the phrase "cobbled-up" will no longer be in your vocabulary. Brakes is just brakes. Once you go thru this, you can find shortcuts. Soon you be here telling fellow FABO-ers the same story, but with a happy ending.
Happy HotRodding