I think having a rifle only 8" longer is being emphasized to much.
It's not "being emphasized to[o] much". From where I sit, the importance of those 8" is being overlooked by someone without experience, despite the good advice of several folks WITH experience.
As a direct experience anecdote, I have AR's in many lengths, from 7" to 29", including my match rifles which are 29", my Pdog rifles which are 22" and 24", my deer hunting rifles which are 18" and 20", my rifle course trainer which is a 16" carbine, and my coyote calling And deer hunting SBR's which are 10.5". The handling and balance change comparing my match rifle at 29" to even a 24" field rifle is a huge change in handling and balance, plus I lose 100fps, which effectively means 50yrds earlier transsonic transition. Swap that 24" for a 20" and suddenly the handling of the rifle is completely different - it stops living as a long range bipod rifle and shifts more to a fieldworthy short to midrange rifle. I gain some handling, but I also lose stability for long range shooting, and another 150fps. Cut that down to a 16" carbine, and carrying and maneuvering the rifle becomes even easier, but now I'm completely out of the 1,000yrd game, because I lose another 200fps...
So here's what those 8" mean to me, scientifically:
1)
Velocity = Supersonic Range: In my 24" barrels, I can push a 73 ELD-M to 2850fps, pushing hard (and abusing brass, 2900), but I struggle to get it up to 2500 in a 16" barrel. That means the 16" barrel falls transsonic about 850yrds, whereas I'm still supersonic at 1,000 (BARELY). I can shoot pretty well to 600yrds with my 16" carbines, but the wheels fall off past 750yrds. Comparatively, I can comfortably get out to 800yrds with a 24", stretch it to 1,000 with relatively moderate success, and the wheels flat fall off past 1,000. With a 20" AR, I can sneak JUST under 1,000yrds before falling subsonic, so ringing the steel at 1,000yrds fits. I have ranges which extend to 1,200 and 1,600yrds, and access to longer if I like - but I dang sure can't capitalize upon those full lengths with a 223/5.56, regardless of barrel length.
2)
Muzzle weight & torque = Stability on target: For a 0.750" gas block, that 8" of barrel between a rifle length 24" and a 16" carbine, both with hbar-esque profiles, weighs almost a full pound and a half more (1.43 lbs). With almost a pound of extra barrel positioned at the end of the muzzle (center of mass 4" beyond the muzzle of a 16" carbine) and almost a half pound more barrel under the handguard, that accounts for a SIGNIFICANT stabilizing torque on the shooter's bipod/rest/support hand, which is lost when shooting a carbine. Using an over-length handguard on the carbine will increase the forward stability of the bipod, but it also cuts down on the stabilizing moment offered by the barrel mass, so it's not a winning proposition overall compared to having that extra mass out on the end of the barrel.
So if you get away from your current position, which seems to be either or both ignorant or arrogant, and listen to folks with real experience - that 8" really does matter. If it didn't, nobody would ever build 24" rifles, we'd all be running around, shooting 1,000yrds with dinky little 16" carbines.
I'll reiterate also - you really won't be able to build a 1,000yrd capable AR-15 for $700, I really don't believe you could build the upper alone for that allowance. What you COULD do, however, is buy a $400 mil-spec carbine, just for the defensive and short range plinking applications, and pick up a $350-400 Rem 700 ADL, Ruger American, Savage Axis, Howa 1500, etc in 243win and still have a very low ammo cost, but be much more capable at long range shooting. The ammo you waste walking your 16" carbine onto target at 1,000yrds will cost more than the difference in buying a blasting AR carbine AND a long range capable budget friendly bolt rifle.
You're trying to make a Pinto into a drag racer, which is difficult to do anyway, and you're hamstringing yourself with a pinto-level budget... If you think you can be proud about hitting a 60" target at 1,000yrds every now and then out of a lot of rounds fired with a 16" carbine, then sure, feel good about that. If you want to ACTUALLY learn how to shoot long range, build an appropriate rifle. You CAN build an AR-15 which drives well at 800-1000, but you really CAN'T build an AR-15 Carbine to do so.