LA 360 budget build ideas

I may have listed the wrong mileage, I'm wanting the gas mileage to be in the low to mid teens
With the 262 type cam , I'd be surprised if you couldn't tune 65@2250 into the hi teens/low 20s. That 262 cam will run and make mileage down to 1800 no problem, if you give her the timing she wants.
When I read 5mpg, I was pretty sure it was a typo... lol. So I more or less ignored it, but high-lighted it so you could catch it.

Five thousand is a nice budget, and you can build a nice dual-purpose engine for that. Just slam some closed-chamber alloy heads onto it, pump the pressure up to around 185psi, up cam a wee bit, and now you got a tire-frying powerhouse, that still gets hi-teens for hi-way fuel-economy, with 3.23s.
More pressure translates to more low-rpm torque, which translates to a smaller required throttle-opening, at no matter what load the engine is seeing. And that means less rear-gear and especially less stall, is needed.
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I had a hi-pressure (185psi) 360 combo back in the early 2000s, with a manual trans mind you. It didn't much care what starter gear it had, and at one point I had it geared down to 3.23 x .71 x .78=1.79 final drive, that on the hiway, turned 65=1450 in double overdrive. But I couldn't give her the timing that she wanted. so I switched to 3.55s, for a final-drive of 1.97 and 65= 1600, and bought/installed a dash-mounted, dial-back, spark-box with a range of 15*. With this and a V-can modded to 22*, I was able to find 48+15= up to 63* of cruise timing; which was just a lil more than she needed. This engine combo made 32mpgs, on point to point hiway cruising, with a Hughes HE2430AL cam, that is ;
270/276/110 and 223/[email protected]; in a 68 Barracuda weighing ~3800 with passenger and gear.
That combo was very sweet, but the cam lost lobes right after an oil-change, back when they took the zinc out of the oil and failed to memo me, lol. So the next cam was one size bigger, still a FTH and I got rid of the Mopar overdrive box. But the 3.55s are back in, and still with the GVod. .
The point is; that with the 360HO as a base, lots of things are possible.
Btw
at one point, that 2330 Hughes cam was running on 11.3Scr, tickling 195psi, and still running 87E10, from idle to WOT, at any load-setting.