1969 Pontiac Firebird

About the car:

Pontiac 350
orig 2 bbl now 4bbl (Rochester Quadrajet)
HO heads
single exhaust 2.25 (sadly)
TH 350 Auto
2.56 open diff (sadly)

My problem is an acceleration issue.
either rolling or from a stop
when I give it between.25-.75 throttle,
the engine stumbles, pops out the exhaust, hiccups, and makes a scene.
But, give it full throttle and it runs like a top.

It has a new fuel tank, filter, and carb.
the fuel pump is probably original

The HO heads put the engine right on the verge of detonation and I've retarded the timing a little as a saftey precation.
I'm thinking that the problem is with the single exhaust and maybe the fuel pump. I'm hoping it's got nothing to do with detonation as a higher octane fuel is not readily available to me.

can someone confirm my diagnosis and/or give me any other ideas?

Thanks