High torque 360 LA build camshaft recommendations

IMO
The big ports and the 1.88 valves are not the problem.
The problem is the lack of cylinder pressure, which translates directly to lazy cylinder-filling at lower rpms.
A cam with a later closing intake valve will just be lazier, and make less pressure. I'm with Rusty, the stock 252* 112LSA cam is just right.
I highly recommend that you do a compression test and see where the engine is at.

With 3.54s and 28s. 65 mph will be 2760 @ zero-slip, maybe 2900 at 5%. Therefore you can run a 2800 stall no problem which is what I would do.
Forget the cam, install the 2800.
The TQ is the right carb for the job.
If you want more bottom end, Your #1 go-to is to increase the cylinder pressure.
There are several ways to do this;
you can increase the Compression ratio. Or you can close the intake valve sooner with an earlier-closing intake valve event.
IIRC the stock 360 2bbl cam specs are 252/260/112. In 4* advanced this will give you a nice small Ica of 54* and at say 7.8 True Scr, that should get you about 128psi at 500ft elevation.
With iron heads you can bump that to around 160psi, still on pump gas.
Follow along with me in this exercise;
Lets say we target 155psi for the sake of towing.
With no other changes, this would require an Scr increase to 9.2.
A stock 360 has a swept volume of 737.21 cc. To get to 9.2Scr, the total chamber volume would need to be not less than 89.9cc.. With 72 in the head and 8.6 in the gasket, yur already at 80.6, so the flat-tops gotta be no lower than 9.3cc which is .045 in the hole. I'm pretty sure the stockers are around .150in the hole. So yur kindof screwed with the stock pistons. However;
the engine doesn't much care how you get these 89.9ccs. You can push the pistons up closer to the deck, or use a thinner headgasket or install heads with smaller chambers, or even shave the heads that are currently on it.
Lets say your pistons really are .150 in the hole(30.9cc), and lets use the .028 gasket (6.8cc). Now yur up to 37.7cc, so then the heads gotta come down to 52.2cc. Can you shave the stockers that far?
IDK but if you could yur just making a lotta problems for yourself in fitting the top end back together. A better idea, IMO is to just buy heads with smaller chambers. Of course the best idea is to just install KB107pistons which will come in at about .012 below deck, which is 2.5cc. Now with the .039 gasket(8.6cc) you are up to 10.8cc, leaving 79.1 for the heads. Which allows lots of room to play with camshafting.
This is just an exercise.
The stock 252* cam will have the potential to powerpeak at around 4500. That means the Torque peak will be at around 3000. That means a 2800 stall is bang-on. Or even a 3000.
The 212* cam that Rumble mentioned is a 260/260/110LSa cam and installed at 104, will have about the exact same Ica, so is another excellent choice. Because it is on a 110, it will have a lil more overlap (40*versus your 32*) which has the potential to increase your power just a hair over the factory 252*cam. The additional 8* of overlap with log exhaust valves is of no great importance. Nor is the extra exhaust duration because it is all in the overlap. It's a great cam, but not much of an advantage over the stocker, which you already have....... if it's any good, lol.
So there you have some things to think about.

If you ask me what I would do, the answer is hands down to raise the piston crowns up closer to the decks. It's just too easy. and you will never be sorry. Whereas if you shave the chit off the heads yur just opening up a can of worms that lead to a domino effect. After the heads go back on you will find out that the intake flanges will have to be shaved, then the china wall is too tall, then the ports no longer line up. So the money you saved on pistons (and probably boring etc) all gets used up in machining, and not every machine shop gets it right the first time.
Yes you could install the 273 heads and get the cylinder pressure you want. And yes it will run just fine. But beginning at around 3500, those tiny ports and valves are gonna put the brakes on airflow and by 4000, like you said, she will be wheezing pretty hard. Forget passing-power which at 55mph will be about 3700 in Second gear. No horses left in that barn.......... especially not at say 128psi CCP,(Cranking Cylinder Pressure).

Ok so now, I gotta tell ya something, that is gonna mess everybody up.
In about 1975, I installed a 340 in a 65 Valiant Wagon. But not yur typical 340. I was 22 and poor as can be, but I recently inherited this junkyard 340 short (no cam), and a complete 1969 318 top end, plus it's cam. So I slapped it all together, installed the only exhaust that would fit, namely Hooker fenderwell headers, and turned the key. Up until my Barracuda,(see Avatar) that Valiant was my favorite all-time combo . It was a GREAT street car. Tons of torque, pulled like a freight train, got stupendous hiway fuel economy, and revved to no end even thru the 2bbl, lol.
But like you said, there wasn't much after 4000.
So what was different about that 340-2bbl?
Well, for starters, it had a boatload of cylinder pressure. Make that a tanker-load. The 318 cam, IIRC is a 240/248/112 and in at 108 has an Intake closing angle of 44*.. Man that is really slamming the door. I never measured the compression on that combo, but it wouldn't surprise me to find out that it was pushing 200psi. Hey, I just remembered something, I still have that engine!, altho it is all in parts, lol. I'll have to go find that block someday and check the date on it.................

Anyway I can almost hear Rumble snoozing in the background, so I'm outtahere, lol.

Happy HotRodding