Two things to look at, the fuel supply first to make sure you have enough fuel for more air flow and second look at getting every part of the car lighter
As far as the heads the more air they will flow with enough fuel will make you more power
I swapped 4 different pairs of heads on my old pump gas Duster, the iron 906 ported big valve heads that flowed 266 @.700 on the intakes made the car run 10,69 at 124. MPH weighing 3450 lbs. with me in it. I put a set of CNC ported Eddy RPM heads on it that flowed 310 CFMM @.700 lift and it went 10.49 at 127 MPH with the same intake and carbs and same compression ratio, I had a fuel delivery problem that I fix and the car then went 10.30.
I had the motor out for freshening and dyno tested two different sets of Indy heads, a set of SR M.W. ports that flowed 340 CFM @ .700 and a set of 440-1 that had a lot of port work done on them that flowed 370 CFM@.700 also. They both had 76.0 CC C chambers so the compression ratio was raised from 10,29 to 1 with the iron and Eddy RPM heads with the 84.0 CC chambers to 10.78 to 1 with the smaller 76.0 chambers.
I used a Indy 400-3 intake on both sets of heads with the same 1050 CFM Holley Dominator, the SR heads made 727 HP at 7300 RPM and the 440-1 heads made 775 HP at 7500 RPM missing from 5200 RPM up to peak RPM due to the dyno header flanges being smaller than the exhaust ports where on the 440-1 heads it wasn't a dead miss, it was intermittent and not the same cylinders according to the EGT readings.
I put the 440-1 heads on a 526 C.I. 440 block bracket race motor I had and those heads made 70 more HP than the SR heads did on the same dyno, more air flow, more power
Make sure your headers will fit and work okay with the heads you decide to get, bigger exhaust flange holes than the exhaust ports are absolutely a must if you want more power Trust me on that, those dyno headers where only around .120 higher on the exhaust flanges on the bottom of the ports than the 440-1 heads where but those headers made those heads miss on both motors from a little over 5000 RPM up
Testing headers on the dyno we found that all the motors, never mind the C.I. size, compression ratio or RPM made more power with bigger pipes
I haven't done the same header testing at the track on a A,B,A test but I have been told by more than one hard core honest Mopar racers that their cars went faster with bigger pipes and collectors at the tracks we both raced on My current car has 2 1/8 to 2 1/4 primary pipe headers on it with a 4.0 collector, it has ran 8.86 at 150.+ MPH weighing right at 2800 lbs. with me in it, 5.50 ET at 120. MPH in the 1/8 mile
BTW, my next go fast bracket motor will have a set of B1-MC heads on it that flow a bunch of air
Good luck on your deal, speed cost money, time and work, how fast do you want to go

I think a fully ported set of -1s, a custom roller, bigger headers, and the -3 intake will get you there. Talk to Dwayne Porter. I was in the process of building a 4.25" stroke version of the same type of setup you have before I bit the bullet and built my KB block hemi. My car is similar weight and I also wanted 9s NA on pump gas.
My plan back then was a 511" RB w/ the big CNC ported Indy -1s.

How about taking some weight out of the car?

If the efficiency of the car remained the same with the new combo as it did with the 10.60 combo....... you’re looking for another 130hp.

I’m not sure that’s feasible with a $4k budget.

A bottle would do it.