the best way to deal with a locked up nailhead core, is to not purchase one to begin with. of course, theres exceptions to the rule, such as getting one for free or super cheap because the core has pieces that you need for your build, or you plan to part it out. "free" isnt "free" if you have to pay someone to take what you don't use, to the dump. yes, you can part them out and make money, but it requires patience and lots of time and space to store the parts, and you have to guarantee every individual part you sell, is GOOD and useable. thats why mystery cores don't bring the same money/have the same value of the sum of parted out parts do, as you arn't, and cant be held responsible for anything that's not visable from the outside. the reason why i don't recommend getting locked up nailheads, is 9 times out of 10, the reason why it's locked up is due to exposure to water. if you go to look at a core to purchase as a good start for a rebuild, and when you show up, the engines clearly been sitting outside, uncovered and or opened up, turn around and leave. the main reason why, is you cannot safely replace the valve seats in these heads, as the seat is too close to the water jacket. even if the machinist doesn't crack the head upon seat install, there's a far more than likely chance the heads will still crack later on under normal service. so if there's excessive pitting to the seats from water exposure, the heads are junk and should be thrown away. because of that, the heads are the most valuable part of your core. most 425s cant even be bored out to .060 if need be. so if youve bought a core thats already rebuilt and then had water damage.. or youve just got a ton of cylinder wall wear already plus the said water damage, then you may end up being stuck sleeving. these days most machinists charge upwards $2,000 to sleeve all 8 cylinders.... when you couldve just started with a better core. 425s arnt bad engines but unless you're building a car that originally came with one, i'd settle for the 401 or one of the smaller nailheads that also cool better.
for the most part, mystery nailhead cores can be gotten for 400 dollars for less, un stuck (in the USA). an exception to that rule would be 425 cores (especially with all the factory dual quad stuff) and 364 engines that are equipped with a four barrel intake. 322s and 264s tend to bring even less, even though they are great engines. the 60s cars are more popular, and everyone thinks they need the biggest cubic inch nailhead to put in a model A, for instance.
what makes a mystery core, a mystery core, is any engine that's unrestored, as well as even "rebuilt" engines which have no paperwork. in fact, with my experience, you are much better off with getting an unrestored core out of a field, than an abandoned fresh rebuild without paperwork. about close to half the engines we rebuild here, are "do overs" that other shops have previously destroyed, or heavy corners were cut, and that's why the person is trying to pass on the engine to someone else. so beware of that! with the price of rebuilding these engines, its very important to assess whether you do in fact plan to keep your car "forever." rebuilding these engines with plans of flipping the car afterward to try to make money, is money lit on fire, and hard to do. unless you've got a very valuable car such as a 53/54 skylark.
first things first, to remove a dynaflow transmission (converter does not just slide out of the front), engine must be free'd up first. start by disassembling the engine by removing the valve covers and rockers, after removing the spark plugs and soaking the cylinders with whatever penetrating oil you have. trans fluid and diesel work well too. everyone has their own method, and its really not that important. never try to use the crank bolt to turn a locked up engine. the crank snout flexes and you have no leverage. USE THE RING GEAR TEETH to turn it with a pry bar up against the bellhusing skirt. you have 100x the leverage. work the ring gear back and forth and continue to remove rockers and lifter to continue to isolate the problem. take note whether the valve are stuck down. proceed to removing the heads completely. if the engines been exposed to water, and you free it up. the damage is done. it's not going to magically be brand new again just because you free'd the engine up and it should be disassembled completely still, to further assess the damage and address it. in the past, ive had locked up solid engines that i stripped completely down to find the main bearing were just glued from dried up white grease. you never know what you're going to find, but water exposure is #1 on the list. if once the heads are off, you find built up rust in the cylinders, scrape all accessible rust and debri away with a razor blade. remove pistons that you have access to, first with a long prybar and a hammer against the inside face of the piston if you are concerned about splitting the cylinder wall during removal, feel free to drill holes in the face of the piston with a hole saw to relieve some tension and stress. i never ridge ream these engines. its never required for removal and if theres a ridge, the engine needs to be bored anyway. if you have no experience with a ridge reamer, theres also a big chance that you end up causing damage to the cylinders by going too far.