Advice on a 625 CFM STREET DEMON CARBURETOR for 273 commando

As to how many cfm your carb will pull, it hardly matters what size 4bbl you put on it; That is to say, if your engine is only capable of pulling 390cfm, then any 4bbl will supply only that much.
The problem comes when the carb gets to be too big, then you have other issues as you have discovered.Mostly related to driveability and starting,just as you have discovered.
It is doubtful that your engine normally aspirated can even top out a 500. So if you want a 650 have at it, but something closer to 500 will be a dream at lower rpms, where it might pull 80 to 250 cfm under various conditions, and under 4000rpm, all depending on load, altitude, temperature, and volumetric efficiency.
If your engine only is able to pull 390 cfm, and you pull it through an 800 carb, it will still only pull 390 cuz that's all the engine can do. The difference is the velocity thru that big carb is about 1/2 of what the carb was designed for, and so you get to mess with all the circuits to optimize it.
If you bolt on a 250 cfm carb it will perform perfectly up to the rpm where your engine is able to pull more than 250. At that point it becomes a restriction. For a 273, this could be around 4000rpm. The engine will continue to pull more cfm thru the small carb, it just can't pull the full 390 to make as much power as if it had the correct sized carb.It might get close if it was held at one rpm long enough, but that would never happen on the street.
So, most of the time you want the secondaries to come in after the engine is able to accept them. This is usually around 3000 rpm or a bit higher. For you this might be 165 cfm,on the primaries. but if your engine power-peaks around 5000 and you rev it to 6000, on account of your automatic has that powerband requirement, then your total cfm might be 390cfm. With an exceptional set-up pulling 85% VE your total cfm requirement might be 403.
With a bigger size cam peaking at maybe 5600 and shifting at 6500, your total requirement might be 436 to perhaps 450cfm.
Remember that these are full-load WOT requirements.
And most of the time you will be on the primaries, so small primaries are a good thing.Since most 4bbls are square bores, a 450 would be well able to pass 225 on the primaries, thus extending your low speed operation to 4000, if the secondaries were disabled.But since the secondaries usually begin opening at about 65%, the primaries are actually gonna only have to work to about 2700 at which time the vacuum secondaries may be triggered.
But if you want to bolt on that 650, it will work. The velocity thru the primaries will just drop a tad as the secondaries open. And so you get to mess with the jetting again. And the primaries may not be as crisp as they could be.
Me personally,I would bolt on a 500 as a maximum. This might be good to 8000 rpm, at 80%VE.
800s are really for over 400 cubers. mean think about it; what size carbs did the factory put on 340s/ that's right 580s IIRC. Those are good to 5900at 100%.
A 750 might feed a 367 to 7000@100%VE. I ran a 600 on my 367 for a while with a 270*cam and it wasn't that doggy.At lower rpms it was actually pretty crispy.A 600 is good to about 7000@80%VE
'Course I am a big fan of 4 speeds and DP carbs, but only cuz my engine can spin the tires pretty much anytime,with those,lol....Lots of pumpshot seems to cure the sag