Let's forget about vacuum advance for the moment.
Keep in mind that as you move total advance, whether advance it or retard it, it will affect your initial timing.
You state your distributor seems to have 30 degrees of mechanical advance. My personal opinion is that your total advance should be between 32-34 degrees. Lemans guy said 36 degrees total, but I think this is too much, but can still work. He tunes distributors and is more qualified than myself, but the most important thing is not having any engine detonation/pinging.
Taking your initial timing of 6 degrees, and adding 30 distributor degrees gives you a total of 36 degrees (6 + 30 = 36). If you wanted to go with 34 degrees as your total, you would do a subtraction, 34 degrees total minus the 30 degrees distributor and get 4 degrees initial (34-30 = 4). Obviously 4 degrees is too low and probably won't work to well.
So at this point, your initial advance is dictated by your distributor advance - they are fighting each other in that if you set your initial higher where your engine will like it, lets say 10 degrees for now, you will have WAY too much total advance (10 + 30 = 40). You say your engine likes 16 degrees total. If we add this with your distributor advance, 16 + 30 = 46, you will be experiencing burned holes in your pistons. So you cannot at this time set your initial advance on anything more than 6 degrees.
Problem #1 that I see is the distributor itself. 30 degrees advance may need to be reduced by limiting the advance of the mechanical weights in the distributor - if you were to set total advance to 34 or 32 degrees.
Now for the vacuum advance. 25 degrees advance from the vacuum seems excessive. Looking at the 1968 factory Pontiac specs (attachment included) shows the maximum vacuum advance listed under each distributor. You will note you only see 10 degrees.
The vacuum source can be either a ported or unported fitting on the carb or to the manifold. Both unported and to the manifold will give you direct engine vacuum.
If you use manifold vacuum (ported fitting or direct to a manifold fitting), you would have too much initial advance. Setting initial timing at the balncer for 6 degrees and then adding 25 more degrees of vacuum advance from direct manifold vacuum gives you 31 degrees initial advance at idle (6 + 25 + 31). Too much. An unported fitting would typically provide no vacuum at idle and not add the 25 degrees, so the engine will be running at 6 degrees initial which is not your engine's preference as it wants 16 degrees initial.
Vacuum advance comes into play under light load or steady throttle cruising. It is constantly changing as does engine vacuum depending on throttle position or load on the engine. 25 degrees of vacuum advance added to your total mechanical (36 degrees here) will only happen periodically and will vary from 0-25 in a constant state of change. It gets added to whatever the mechanical advance happens to be at specific RPM's. So for example if you were puttering along at 2,300 RPM's, you have not yet reached your total mechanical advance of 36 degrees because total advance does not come into play until you reach 3,500 RPM's. You might have a total mechanical advance at 2,300 RPM's of 28 degrees. Then when you let of the gas pedal, maximum engine vacuum results and you would now take your 28 degrees mechanical and add the total 25 degrees vacuum for a total engine advance of 53 degrees (28 + 25 = 53). My opinion from my reading is that around 50 degrees total engine advance is about where you want to be. But in any case, you have 53 degrees in this example. If the engine begins to surge at light throttle, then try reducing the vacuum advance total.
Now lets wind the engine up through the gears. Once you go past 3,500 RPM's and continue on your way to 5,600 RPM's, your engine has reached maximum mechanical advance (3,500 through to 5,600 RPM's). You momentarily let off the gas to make a shift for the next gear (assuming you are not pulling a fast hard slam-bang speed shift). When you let off the gas at any time after 3,500 RPM's (maximum distributor advance), engine vacuum soars to its maximum for just an instant and your vacuum advance kicks in for that instant. What you now get is your 36 degrees mechanical advance plus the 25 degrees of vacuum advance for a total engine advance of 61 degrees (36 + 25 = 61). Yikes! Way too much. It is possible that this is where your problem is coming from.
Going with a different vacuum advance that limits the total vacuum advance to 10 degrees and which has been suggested, would be the correct way to go. 36 + 10 = 46 degrees total engine advance. A little shy of the 50 degrees, but better than 61 degrees.
Problem #2 as I see it - incorrect vacuum advance as used with your total mechanical advance of 36 degrees. 25 degrees of vacuum advance is too much.
The above is to illustrate what I see is happening.
Next, you mentioned setting your initial at 6 degrees and letting the 10 degree vacuum advance can pull your initial up to 16 degrees at idle. This should work IF you connected the vacuum line to an unported fitting on your carb or directly to your intake - both of which would be drawing off full engine vacuum. So initial would be 6 plus 10 from the vacuum advance for a total of 16 initial advance (6+10 =16) and puts you were you want to be. Some engines like more or less initial, but if 16 seems to be best for your engine, then keep it there.
If you switch to a different vacuum advance can, you will also need to know at what engine vacuum it operates. Some will provide maximum vacuum advance at 10 Hg, or 13-14 Hg, or 20Hg of engine vacuum. The vacuum can may not add all of its timing at idle. As an example, you may have a can that max's out at 12 inches of vacuum while your engine was only idling at 10 inches. So you want to check the amount of vacuum advance supplied by the can at idle and you want to match your engine vacuum with the 10 degree advance type cannister.
Modified engines with more cam that generate less than 15” Hg. of vacuum at idle need a vacuum advance can that’s fully-deployed at least 1”, preferably 2” of vacuum less than the idle vacuum level so idle advance is solid and stable.
Another option is to install a vacuum advance stop which limits the amount of movement of the vacuum arm that pulls on the distributor plate.
My Conclusions: I would go with 34 degrees of total advance, but if 36 works and you are not getting any detonation, leave it for now.
Get a vacuum can that has 10 degrees of vacuum advance OR get a vacuum advance stop.
Keep your engine timed for 6 degrees without the vacuum can hooked up to set it and then connect your 10 degree vacuum can to direct manifold vacuum to give you the preferred 16 degrees initial at idle.
This should get your timing on track. Test it and see how the engine performs. If you still have issues, just for fun, drop the total timing from 26 degrees down to 34 and then 32 to see if this cures it. Don't worry so much about your initial timing (which will drop proportionally to 14 and then 12 degrees), you are just trying to adjust total mechanical advance to see IF it cures the problem. If not, go back up to 36 degrees. If it does, then you will have to limit the amount of mechanical advance in the distributor so you can return your initial back to its 16 degrees.