New heads, old bottom end?

I think it depends on how you are planning to drive your car. If it's going to be a boulevard cruiser that isn't going to see much in the way of stress and high RPMs, then I think it would be okay. Just don't be tempted to "get on it" too hard just because of it's improved performance. I'd also swap out the old timing chain with a good quality roller to be on the safe side.

Back in the 70's I put rebuilt heads on a <100,000 mile small block Chevy. Immediately started using a fair amount of oil so I tore it down and rebuilt it. You may be luckier but I think more often than not they'll use more oil.

i know it's a 'next level' move but if the heads are off, pull the short block an refresh it on the garage floor if need be. a cheap engine stand is a plus but $ can go for parts. rent a berrybush hone, wash the block on the driveway or at the car wash (after hours) and give it a fresh set of bearings, rings and timing set. if the oil pump worked before use it again. worth every penny. if the cylinders are extremely tapered / worn at the top it'll suffer at rpm, consider having it bored / honed the next oversize and new pistons to suit

At Dad's shop between '74 and '92 we put new or rebuilt heads on all sorts of high mileage bottom ends. Especially the Datsun and Ford 4 cylinders which seemed to blow head gaskets or strip timing belts with regularity. We never had any complaints about our repairs.