Having just put one back on the road after over 10 years in a field, I will add my .02
I was fortunate being able to do most of the work myself as it would not have been cost effective otherwise. I think your $10k budget will be quickly blown out of the water from all the stuff you didn’t think about. If you have another mechanic do the work, items like belts, hoses, battery, cables, fluids, engine mounts, tune up parts, etc. will be replaced. Considering the age of the vehicle and how long it sat, these are prudent purchases. I bought a new alternator, starter, a/c compressor, radiator, fan clutch , heater core, a/c evaporator. A/c hoses and a/c condenser just because when I closed the hood, it was done. A quality reman engine isn’t cheap and almost rare today due to the quality of parts. I found a used GM Goodwrench engine with really low miles. Good, reasonable mileage, small block Chevys are rare but out there. I highly doubt you would ever drive the truck enough to recoup the expense of the quality reman. Current independent garage rates here in West Phoenix go from around $175-210 an hour. Having been a manager of an auto repair facility, I would quote it as time and materials with a guess of around 20-24 hours labor to R&R an engine with no accessories. By the time they had the mark up on parts, 3/4th of your budget is gone
You mention “fuel tanks”, back in the day when people daily drove these 8-12 mpg trucks, the dual tanks were necessary. With it being a third, limited use vehicle, I would only put one back in it just to keep it simple and the expense down
I am not a big fan of headers on a daily. Everyone will chime in how they have never had an issue but I don’t want to deal with the blown gaskets, I would leave the manifolds on it and have a new exhaust bent up for it at a muffler shop. The Summit one you quoted is great for a DIY person with a welder and some experience doing it but having a muffler place bend pipes to go around the transfer case and it doesn’t rattle or fall off when your done keeps your life simple.
Due to the age of the vehicle, I would redo the entire brake system just because of safety and reliability, it’s not that expensive. Reman calipers, rotors, pads, repack wheel bearings, shoes, wheel cylinders, drums, master cylinder, flexible brake hoses etc. Go through the front and rear suspension, replace worn parts, shocks and spring bushings as needed. Change the u joints or grease them if they have been replaced once, change the oil in the differentials. Make sure the transmission isn’t leaking and verify it works, address that as required.
I recently sat down and itemized all the receipts from the purchase and building of my truck, to say I was shocked was an understatement. I enjoy it and tell people it keeps me out of the bars and pool halls at night but the truth is it's an expensive hobby and not cost effective to have somebody else do repairs on it. It's difficult to bring them back after sitting that long.