Sorry for the late reply. Werby pretty much hit it all though, I'll write a little book though
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First, look at most any head and piston other than a hemi. Even the lowest compression engines have a flat pad on the head and if possible a matching flat pad on the piston. Modern thinking has even gone away from a standard "dish" (except in very purposeful choices) to an "inverted D-cup" which is basically a copy of the quench pad and combustion chamber.
The issue of course is we have to package everything along with a fixed location of the valves, multiple valve sizes, etc, so it's not perfect, but you'd like the smallest combination of head chamber and piston cup you can. Not in terms of volume, volume determines compression ratio, but in terms of direction in each way, length, width, etc and as clean of a path across the chamber to allow the mixture to move around as well as the flame to travel quickly. (no domes, bumps, funny shapes)
Then, everything that is NOT that combustion space, you would want to almost touch at TDC in operation.
Think of what happens in the cylinder, piston drops, atmosphere and cam overlap starts filling the cylinder, the cylinder rises, the air and fuel is compressing, and when the piston's quench pad(s) and head pad(s) almost smack into each other, all that air and fuel is churned, tumbled and forced into the chamber/piston cup. Some people actually call them "squish" pads, not quench
Then the engine fires, that chamber has a small distance for the flame to travel. The air and fuel is nicely mixed up burns evenly, and it starts pushing on the piston as heat rises and gasses expand. The benefits are 1: Everything is churned up and one place, 2: a neat clean "chamber" allows a fast flame front 3: the complete burn means less chance of detonation, the clean edges and less surface area can mean less chance of preignition. This is better everywhere. You even need significantly less ignition timing.
Then think of something like yours, piston rises, it starts to move things around, but only goes to a certain point. Additionally, when it fires, even at the same compression ratio, the flame front will have to travel across 4 inches of bore, and 1/2 way across that, it will hit the edge of the chamber in the head. To counter that, you need MORE advance to fire early enough to make power. Ironically though, because there is some unburned fuel near those shadowed spots during burn and maybe some that didn't get churned up nicely, you have a significantly higher chance for detonation (ignition from heat after the spark plug fires).
If you look at builds around the dyno pages, look at a modern chamber/tight quench, they can get to the point where they only need 24 degrees of timing to hit max power, but the looser versions need 40+ degrees of advance.
The ironic thing is, the engine that
requires more advance, is less likely to tolerate it, that's the punch line for you. Until you get significantly tighter, your engine will want more and more advance, but it will likely ping. So raising compression is OK, and recurving is OK, but one is a lot cheaper than the other, so I am trying to find you some "free chicken"... basically what can you do to live with it and spend little right now.
There are also benefits on the exhaust stroke, same thing but think of exhaust rushing out of a smaller area and being pushed that way, reducing hot spots and giving a more focused area during overlap, but the compression stroke is good to picture the majority of the benefit.
So now, I keep preaching the ignition advance. Going back to the loose quench scenario. Ford uses and real slow advance and late initial. If you can get the timing to start at a higher initial, and come in a bit quicker, but not so quick that it pings, you will get some part throttle power. That would cost 100 bucks max and will make some difference, it won't turn it into a 390 or 427, but it gets some noticeable snap
Now I disagree about the benefit of headers. However, I agree that you likely shouldn't buy them now. If you sized the proper header for the engine, during your 40 degrees of overlap, it would fill the cylinder slightly more than stock exhaust will. It's not a backpressure or flow thing, it's a negative exhaust pulse thing. The problem lies that if you buy headers for the current engine, they would need to be very small diameter and as long as possible. When you build a 390 or bigger, they may be too small. That's the only reason I wouldn't buy them (and they probably don't make a tiny header for your car)
However, don't be discouraged, because if you decided to make some power, as Werby showed, you could get a 390 crank and rods, a the right set of pistons and you'd be making a lot more torque and power. Additionally, you could even just buy a set of pistons and rings and make yours a modern 352 build, however, I think most would agree that sticking a 390 or 428 crank in there is better power per dollar.
Last comment, I do like the idea of just bolting it back together and running it (of course I would add a distributor recurve...insert dead horse). Using your numbers, going from .132 quench distance to .106 is a waste of expensive head gaskets when you can buy a single 8554 for 15 bucks. At that point, checking TDC with a piston stop and making sure your balancer/pointer is correct and having initial up near 14-16 with mechanical coming in quicker, you'll be happier and have some coin to save for the next step.