Peeeot -One of our members - "oldcarmark" - once had a problem that I was reminded of as I read the various symptoms of your outfit. Initially, it wouldn't shift from park to drive without staggering and stalling ('56 sedan with 390 cfm Holley installed). The problem didn't turn out to be singular - it was many - and the sum result was an engine tune that
didn't produce enough idle torque at low rpm. He could speed it up (to raise the idle torque) - and it would then slam into gear and stay running - no good, not a solution. He was very frustrated trying to get a handle on this - too many variables. On yours, it would seem the addition of heat decreases the idle torque further and makes the problem get worse - another variable.
His outfit had:
(1) Unsuitable spark advance - initial, increase rate, and total mechanical.
(2) Vacuum leak (excessive PCV passage in that case).
(3) Carburetor idle set-up incorrect (for his new Holley).
When a "tuner" takes on an engine/vehicle combo and works it up for a customer - they can take a "ho-hum" carbureted engine and literally make a whole different animal out of it. Most start by getting the ignition in order and going on from that. From the depth of investigation so far - you must have some useful components in hand - coil, condenser, cap, wires etc. I think you can do this tune-up yourself - just start with the distributor and go from there. For pros it is nearly always step one as the spark advance will dictate the carb tuning.
So what is the maximum mechanical advance in your distributor? - I'm assuming the flyweights are in good working order. If you "power time" the engine - determine the maximum mechanical advance by raising rpm until it stops - what is it? These Y blocks without special or reworked cylinder heads like a 36º maximum when there is no vacuum advance connected. If you set the timing at 36º (elevated rpm necessary) and allow it to return to idle - how far does the spark advance drop? This might require placing an auxiliary upper mark on the damper by measurement from the current "0".
Factory set-ups of the era had initial settings at idle of 6º and such. The engines actually produce better idle vacuum (and still start nicely) when that initial number is 10º and higher. Some of our clan are running as much as 14º+ initial with the Ford "timed" vacuum ports in use. In any case - the combination of your chosen initial and mechanical (only) should add up to no more than 36º. You will find that the engines run a bit cooler at idle when the timing is advanced as discussed here - the 6º is a bit retarded and builds water temperature from wasted heat. To get the distributor to operate in the desired advance range - from the initial you choose up to 36º - will take some alteration of stops in the flyweight mechanism. We can help you with this - the mechanical advance tuning is exclusive of the vacuum so that must be inactive.
The engine speed at which the advance can be "all in" - the rate of advance without "knocking"- is tied to compression ratio and gas quality. Swapping springs in the flyweight mechanism makes this happen. To be conservative, try to make the 36º be all in at 3000 rpm or there abouts. Getting the early spark curve correct can add many foot-pounds of torque to your engine - its worth the repetitive teardowns (if you don't know a guy with an old Sun machine). Ask Mark about this operation - he can probably field strip his distributor faster than I can explain the steps. You can get a variety of advance springs from various sources - Mr. Gasket #925D will get you a few choices.
Test the vacuum pot on the distributor to see how much advance it provides. With the engine running a fixed "high idle" speed and stable vacuum - apply manifold vacuum to the distributor and see how much it alters the spark advance. I've done this before with a long piece of tubing and another (high vacuum) "donor" vehicle running alongside. There are other ways to get the vacuum source - just try and be cognizant of the available change when it comes into play. A lot of the pots are adjustable if the upper end turns out too high when the vacuum advance sums with the full mechanical.
Next go to the carb and make sure it is in good condition to take tuning - float level correct - fuel pressure normal. Rule out every possible source of vacuum leak - my own experience has included poor fitting manifold gaskets, worn throttle shaft bushings and passing excessive air through the PCV. If you have PCV installed, a quick change is to simply plug the hose and shut it off at both ends, carb and manifold both. I used a 'Standard" '64 292 truck PCV on my outfit and it would literally run on the PCV air alone (throttle closed) - not good - had to orifice the hose to make the carb work correctly. It has to provide just a small amount of fuel to mix the PCV air - if the requirement goes too high, the mixture screws won't work in the proper range. If your engine doesn't have a PCV fitted it won't face this problem and you must look elsewhere.
This can go on and on - but the advice is to get the various "systems" functional and answering adjustment - and then optimize the next and so on. You will eventually reach the point where the engine produces the necessary torque to run at low rpm hot idle, in gear.
Steve Metzger Tucson, Arizona