The H engine code letter is a Chevrolet 305, which means that you could swap in a 350 and it would look exactly the same on the outside. You may need to replace the carburetor and PROM/ECU with a 350 version.
But behind a 305, you could upgrade to a 700-R4 from a 1988-1991 Chevy car or 2wd truck. The lower 3.06 first gear would wake up the performance and give you an overdrive without changing the rear gears. If you find the PROM from a 700-R4 donor car, it will lock up the torque converter. Otherwise, you can use an aftermarket pressure/vacuum lockup kit.
Very nice survivor.