Must, isn't this an engine that was supposed to have been rebuilt just recently ? If that is the case, I hope you're going to a different shop this time. I'd leave the shortblock in the car if it were mine. If you can still see the cross hatch pattern in the bores, they're probably still okay. And your rings are tougher than you might think. How about draining the coolant contaminated oil from the engine, then cleaning it up, oil the bores and just do the heads ? You'll need a decent gasket scraper, no a putty knife or spackle spatula won't do. Get a good scraper from Goodson or somebody, one of the ones that has the 90* edge blade. You need to clean the gasket residue from the decks. Your engine was obviously running with some of the gaskets leaking coolant into the ports or cylinder bores. it looks from the pictures that it ran that way for awhile.
I'd be careful where you take the engine, or just the heads, to be worked on. From your description of the 'mechanic' who couldn't get the car to run, there may be some guys with shops out near you who just don't know what they are doing. Unfortunately, that is distressingly common.
When you talk about getting a valvejob, or a 'full rebuild' on the heads, just what are you thinking of having done ? Its kinda of scary and irritating at the same time, but there are still some guys out there with a stick and a jar of paste, who believe, with all sincerity, that they can do a valve job for you. They can't. If you brought your heads to the shop I'm with, they would be disassembled, baked and blasted clean, mag'd for cracks, and if okay then you start the work. The valves are measured, and if the stems are okay, they can be reground. If they are bent or the stems too worn, you have to get new ones. Then we check out how are the guides. If they're too loose, ( usually they are ) we bore them oversize and press in a thin bronze sleeve. The bronze sleeve is then broached and/or reamed to the size needed for the valves. The intake valve seats are then cut for three angles. First the seat itself, then the top cut to get the contact lines where they need to be, then the throat cuts cut to get the seatwidth you want. . On the exhaust side, the original seats are cut out and replaced with a hardened insert. Then the insert gets cut to three angles, just like the intake had done. Don't let anyone tell you you don't need hard seats under the exhausts. You need them. Many decades ago, one of the petro companies ( amoco ? ) used to sell gasoline with something other than tetraethyl lead to protect the valves. I don't know if they still do that or not, but unleaded gasoline has been the standard stuff for so long that you may as well get your engine ready for it. Thats what every auto manufacturer is planning on you purchasing, and thats what all of the petro companies now sell. I made quite a nice living for awhile redoing valvejobs from guys who just got a 'fresh valvejob' from someone else and the engine had trouble less than 10K miles later. You need the exhaust seats. If you had the place I'm with do the aforementioned, you'd probably spend about 400~450$. The exhaust ports could be opened up abit if you want. The design is fine, but the castings frequently have lots of cast iron 'boogers' and junk in the ports. You could add thread in rocker studs if you want.
I'm not sure how your gaskets were installed, but they were leaking. Do you have, or can you borrow, an nice click style wrench ? And what kind of gaskets were on there ? I prefer and have had excellent luck with Fel-Pro Blues. But even the best gasket won't help if they aren't torqued down correctly.
It looks from here that maybe you are making this harder than it has to be. Like maybe the engine, after it was redone, has had leaking gaskets the whole time ? Who assembled the engine ? Do they have some responsibility here ? before you tear into the heads, can they be checked on a vacuum table ? I'll go out on a limb and presume that one of the cylinderhead rebuilders in your area can do this for you......and if they cannot, maybe you need to find someone better to work on them ? Keep us posted. LSG