But my guess is that your problem is gonna end up being a fuel issue.
Usually a hot-start issue can be traced to the engine being rich..... and your fine cold-start sorta points to that..... but we don't know a thing about how your choke is set.
But since you say your carb has fuel, it could just as easily be lean.
Next time she's hot, before you shut it down, increase the idle speed to ~1000/1200 with the speed-screw and stall it out. How does it hot-start now?
My guess is that your tuner gave your engine too much idle-timing, which caused the idle-speed to be too high, and so he closed the throttle, which partially shut off the transfers, which then go lean at idle. To get the idle fuel back, he opened the mixture screws. So then it idles ok. But with the transfers as good as dried up at idle, she won't start. That's a guess.
To get your transfers working again, you will have to take the carb off and reset the speed screw such that the exposure underneath the blades is about square. Then reset the mixture screws to in the middle of their adjustment range. With a Holley this is about 1/2 to 3/4 turn out. All others are about 2.0/2.5 turns out . If your idle-speed ends up being too high, you will need to retard the timing. After this, it should, if the wet fuel-level is correct, jump to life.
BTW
With stock-compression and cam, and the factory-type distributor; it is impossible to give your engine the cranking and idle-timing it wants, and still have the power-timing not get her into detonation ....... so I wouldn't even try. Some to most SBMs will like idle-timing as high as 30 or more degrees. The only way to get this is to use the Vacuum advance running full-time on manifold vacuum. But with a stock-type engine, she is almost sure to rattle upon throttle tip in. If you set it this way, the only way to slow the engine down at idle, is with the speed screw, which shuts off the transfers. So then you get a big hesitation or stumble every time you go from idle to off-idle, as the transfers switch from passing air, to pulling up fuel. The transfers are your primary low-speed fuel supply, so they gotta be working. The mixture screws are just trimmers, and used mostly just at idle. If your "trimmers" are rich, she will be a pig on gas and sluggish at tip-in. and she often starts to give hot-idle issues.
Don't underestimate the wet fuel-level which not only has to be correct, but it also has to be consistently so. If you have a solid-lifter cam, the lash will make a big difference too.