"I hoped I could get in through the woofer and then push out the tweeter."
I wouldn't fool with the woofer. They probably isolate it so even if you get it out, you may have no access.
The tweeter is just stuck on from being in place for so long. I don't know what you have for tools, but if you are willing to spend about $10 give or take, get a cheap set of automotive picks. They're sold everywhere. (Lowes, Home Depot, Sears, any auto parts store). They come in a set of 4. Depending on how stuck the tweeters are, you'll definitely want the options a set of 4 gives you.
I think your tweeter has 2 sets of screws; an inner set and an outer set. I would remove the outer set first. Take a 90 degree pick and carefully insert it into one of the screw holes, and when you have it secure, gently pull and the whole thing should come right out. If its really stuck, or you are having some kind of unforeseen difficulty, remove the inner set of screws. Those screws actually hold the tweeter itself to the mounting plate. Separating the 2 pieces may make it easier to remove. But you have to be very careful. If you pull the mounting plate off by itself, the tweeter may fall out of the speaker and scratch the wood finish if there's too much slack in the internal speaker cable for the tweeter. Either way, its not a difficult job, you just have to be careful more than anything.
