Answering some of the comments above...
Searching eBay, I got quite a few matches for Genesis tweeters. There is one pair with black faceplates, and another pair that are with a bunch of other tweeters and midranges that have the masonite plates. I would guess these would be more suitable for my speakers, since they have masonite plates with other tweeters mounted in there.
I'm just curious though. If these aren't the original tweeters (and opinion here seems to think so), whoever put them in seems to have done a good job with putting the metal screen on, unless they were like that already. I will pull them out today and have a look at the back, and post pictures.
I sent a PM to HomerJSimpson regarding the green surrounds. I also e-mailed Rick Cobb.
My cabinets are vinyl, but in very good condition. Sticky though, very sticky, I will try cleaning them today.
I can't wait to get them fixed and hear how they sound.
Lee.