Incorrect Timing Adjustment causing heat issues?

Did the shop have a chassis dyno that can be loaded?
Or an old emissions dyno?
Otherwise its just guess work.
Consider it ballparked, but not tuned.
AFR should not be targetted except for emissions reasons and when given factory specs for a particular condition (usually idle).

The first thing to get correct is the timing. Then work on fueling.
On a hot rodded engine this can be an iterative process of tuning timing and caburation for each of the steady state conditions.
Since this is fairly factory, I strongly suggest going with the factory timing curve. They put a lot of effort into testing and tweaking for best efficiency under all conditions. So that will save a lot of time and effort on your part.
For '67, which is the earliest book I have, the 273 4 bbl has a different timing curve than the 2 bbl. But it also had a different cam and compression.
My suggestion for this fall is that IF the distributor is the original, go with it. Set the initial at the factory recommended as you have. Tweak it slightly (2 degrees) if there is a reason (such as pinging under wide open throttle). One caveat: If the idle speed is much higher than the factory spec, this can throw off the entire timing curve. Second caveat: The initial should be set with the vacuum advance disconnected and the hose connecting to the vacuum source plugged. Golf tee makes a good plug. That may seem obvious but less and less people seem to know this. I know I had to be told this 30 years ago. In the newer cars (70s and 80s) the factory tune up info usually states this but I don't know if it explains that in the '65 shop manual or not.

Next.
A compression check was suggested. That's a good idea but a fair amount of work. I would probably pop the distributor cap and look at the points next. Maybe run a piece of paper between them. I know its pain leaning across the fender, but that's what I'd do next. Then probably look at the spark plugs for any obvious differences. You're going to have to pull them anyway for the comrpession check.
Where the compression check is probably leading is to valve adjustment. Some people might go right to that, then do a compression check afterwords if needed.
Do whatever fits your skills, timeline and preferences.

Back to the fuel mixture.
Tune for Performance.
Performance defined as power, torque and engine efficiency.
This requires systematic trials

Start at the idle and work up.
Idle and off idle are your foundations.
Performance here is going to be revealed by how little throttle is needed to keep the rpms with load.
(manual) to get into first gear without stalling.
(automatic) lose the least rpm when placed in drive. Alternatively have the best vacuum at a given rpm in drive.
Adjust the idle mixture screws 1/8 turn at a time toward lean (clockwise) until the rpms fall off a little.
Adjust them back from that point 1/8 a turn. Check vacuum and or rpm going into gear with your foot on the brake.
You can try another 1/8 turn richer and see if there is any improvement. etc.
If the idle rpms went out of range (higher) with the new mixture, then you can idle speed screw slightly (transfer slots), and check repeat the above excercise.

Next confirm off-idle has good performance by very slowly accelerating from stop with no hesitation. This test minimizes the role of the pump shot and focus on the idle circuit's begining of transition.
If that's good, then test more normal acceleration (for public streets) from stop to make sure the pump shot is not too much or too little for this basic job.

Then you can test out steady driving at various speeds. The fuel ratio at steady interstate highway speeds is determined by main jet and the rods. Steady cruising on local highways
(up to 50 or 60 mph) will still be at least partially using the "idle circuit". It shou;ld be really called low throttle circuit but too late to change that. LOL.
If its too lean while cruising, it will surge. Slow down and take it back to garage. With the Carter type design the high speed cruising restriction is based on the rod and jet combination. Either change the rod or the combination rod and jet. For Edelbrock carbs, edelbrock provides a chart each model showing which combination is needed to make it richer at cruising from whatever combination is in that carb now.

If you have access to the strip or dyno you can test wide open throttle in top gear. AFR is controlled by the jets plus the step up circuit.
If the tune up shop ahad a chassis dyno, that may be what they did for jetting.
All the above tests are effected by timing. If you change timing at a given rpm and condition, then retest before change fuel mixture for that condition.

A good overview of the various circuits in a Carter type carb is in the 1966 and 1970 Chrysler Master Tech "Carburetor Fundementals"
Master Technician Service Conference - Chrysler's Training for Mechanics
A little more about AFR for different conditions is this post
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