I don't mean to sound like an ambulance chaser but it might be time to 'lawyer up' as they say in Texas. A free consultation with a lawyer might tell you which way to jump. Check with the better business bureau and see if the company has had complaints before. Put an ad in the local paper asking for other prople that might have had similar experiences with the company. If the co. sees that you are looking for other customers it might (or should) tell them that you are looking to make a legal case against them. This might help them to see your side. If the company is a relatively small independent one they might realize that it would be better to pay the mechanic's labor on a valve job at $20 an hour or so than to pay a lawyer $300 an hour and stand a chance of getting nothing. To pay a lawyer $100 to write a preliminary to the co. might be enough to show them that you are in it for the long haul.
The advantage that the shop has is that by you signing the work order they have the ability to put a mechanic's lien on your car. Without a lawyer the only bargining point you have is the shop owner's own morals and ethics, of which, apparently, he has very few.
I have worked on cars for about 45 years and this sounds like a classic inexperienced mechanic screw up that the garage is trying to get you to pay for. You are at a distinct disadvantage because they have all the parts (evidence) and can claim that, 'well it was like that when we found it'. You can't prove that your car ran perfectly before it came in anymore than they can prove that it didn't. But, they have the advantage. They can pick up a hand full of bad valves from the scrap bin and swear that these came from your engine.
The only way that valves get bent is from some outside force, i.e., out of timing, or foreign object in the cyl. Valves just don't bend on their own. Valves wear and burn and get carbon on them, but they don't just bend over time. Get your old timing chain if you can. A good mechanic can tell you if the chain is worn enough that it might have caused the timing to jump. I assume that you still have the original camshaft sprockets in the engine. At 120k miles neither should be worn enough to cause the timing to jump.
Good luck, and fight a good fight.