I don’t know much about MSD distributors, but I know the (newer) factory appearing Chinese made distributors that fit our car has flimsy lightweight counterweights that will do just what you are describing. Even the later model Mopar Performance distributors use the small weights and are also “troublesome”.
The thick and heavy Chrysler style weights.
The thin and troublesome weights used today.
Another thing I run across is the grease used in the distributors get hard after a few decades and I’ve seen that cause the ignition advance to do funny things.
The first thing I would do is either purchase, rent or borrow a timing light. If purchasing one, getting one with a dial-in advance is nice (but not a requirement).
Then watch the timing at idle. If this is a fresh rebuild and you have a new timing chain, then the timing light should not vary much. Loose timing chains can cause the timing jump around a few degrees, at idle – which can affect timing a bit.
On most cars (not just Chrysler), the (centripetal) weights in distributor shouldn’t start to move until over 1,000 RPMs (most cases at 1,500 RPMs).
If you have a Mopar with the skinny weights in them or an older one with rock-hard grease in it, then that could be the problem. If ignition timing is varying at idle (because of mechanical or vacuum advance) then that would be a valid reason for your timing to vary that much.
I don’t have an as extreme issue as you have, but the distributor weights on my ’77 wagon needs to be cleaned and re-greased – but I’m going to wait until something else in the area needs repaired, first.
If you have the “skinny/wimpy weight style distributor (aka: Chinese built) – then the only recommendation I have is to find an original Chrysler distributor and install and that most likely will fix your problem (but your MSD might be a factor). As to which distributor (advance curve) to get depends on your current application. If you have a highly modified small block, I would look for a 340 or 360 HP version. The rest of us, I would look for a 318 (2-bbl) version. Either version need to have a vacuum advance on it. If not, stay away (for Lean Burn or computer-controlled versions, which also has no mechanical weights inside).
If you purchase an older distributor, but before you put it in use, I recommend taking the top half apart (see top picture), cleaning well, add grease to areas the weights contact (pivot points, etc.) and a drop of engine oil where the two shafts touch (under the small felt under the rotor), test the vacuum advance (for leaks), install and set ignition timing, and call it a day (if test drive is good).
I have two almost new small block distributers (and a 3rd brand new one) in my garage with the skinny/wimpy weights (of Chinese descent) that I took in trade (for the older ones) - that “I” refuse to use. The older ones fixed their problem(s). I suspect the same will work for you (if you have a newer distributor). I don’t have any more, older distributors, either (for small blocks).
If the vacuum advance is disconnected when idle fluctuates, then there is not much else it can be to cause that drastic of a change.
BudW