Falling on face/missing/backfiring (through intake)?

[Ride The Snake!]

I believe I must have a carb issue on my '70, but I'm wondering what you all think. I've just been sorta teaching myself how to work on this thing for years.

Anything above light demand on the throttle causes the motor to miss or sputter, or more violently backfire--out the intake? Sudden, moderate or heavier acceleration is most likely to induce the backfire, but even if I very gently rev the motor--cruising or stationary--it starts to stumble and miss past a certain point (no tach but I would estimate in the low to mid 2,000s). Progressively, slowly increasing rpm just causes the problem to become more pronounced and often induce a backfire.

Basic-ass stock 350 setup except for a slightly better cam grind:
-Roch. 2G (replaced with a remanufactured unit maybe 7 years ago, after I had attempted rebuilding the old one twice and found no improvement in whatever issue I was having at that time). New carb has maybe a few thousand miles on it.
-GM HEI (I rebuilt it a few years ago)
-stock GM heads from '74
-the Crane cam is nothing inappropriate to the application, I would have to look up the specs but it's a bit of a lower-end 1500-2200 cruising rpm type for trucks
-4 spd MT

-I did the timing kit with a dual roller at the time of the camshaft.
-Last week replaced fuel pump, filter, and sending unit.
-A few years ago (and few miles since) I replaced every part of the HEI including the pickup coil. Plugs gapped, wires look good.
-Timing set to 12 BTDC, no digital timing light or timing tape but the mechanical advance seemed to come in appropriately or within ballpark.
-Idles fine and at low rpm seems to cruise okay.

It must be running lean somehow, no?

If I've left out any other pertinent info just ask. I appreciate any input.