I replaced both hatches on my '86 340EC. I had intended to buy replacement parts as eddiezuskin did, but found that they were no longer available for my OEM Bomar hatches. I don't know what year they changed the handle design, but my friend's '89 340DA has a newer design.
I bought new Bomar pieces that were exactly the same size as my originals from Boater's World. They were something over $200 each, maybe $500 for both, as I recall.
The factory sealed them with silicone, as they did pretty much on everything else on the boat. Removing the screws and then 'cutting' the sealant with a sharp putty knife as you gently pry up on the hatch will get them out. The silicone then needs to be removed from around the hole; I think it's Boatlife that makes a good silicone removing solvent. I then used 3M 5200 to seal my new hatches, though it could be argued that 5200 is overkill. If I need to remove them ever again, cutting the sealant works well, just like cutting urethane to replace the windshield in your car.