Awkward Date - Need Fast Advice!

For me that would be a dealbreaker, but obviously you're considering it. I mean if you want to have kids with her that would not be possible unless you adopt or have a surrogate parent.
It seems you have to really think about what you want. If it's okay with you then go for it but I would slow on the intimacy part and have the sex talk.
I have friends who are transgender and a lot of them deal with their issues through having sex and I know this is a big issue in that community. This may not be the case with the person you're seeing but I'd find out first. I mean is she like that with all the guys she meets or it just you?

Truthfully i dont want to be in bed with her much at all, but i dont know a tactful way to turn her down - ill go to the meeting tomorrow, i owe her that much, but i think that dual gender thing is just a bit too much to deal with.

I would turn her down before meeting tomorrow. I don't think you owe her anything but to be honest. I think that's the more polite thing to do. I mean both of you have to get ready, drive etc but for her it will be with the potential of having an amazing time and for you it will be to break up with her. It's much easier to say I don't think we're going to be a good match over the phone then it will be in person.
The dual gender thing is challenging and obviously she's not the one for you so keep it moving and tell her as soon as possible. I'd call as soon as possible if I were you.

Problem - she's already asleep for the night and probably won't be up until just before the meeting tomorrow. What now? sigh - the double gender thing won't work in the bedroom but i wish there was a way to do this without hurting her feelings, she seems nice, just a little unusual down there.

I would send her a text first thing in the morning asking her to let you know when she's up. When she responds or it's a decent hour to call I would let her know. I think a lot of guys think women are devastated when a guy isn't interested. Yes it may hurt a little but seriously you haven't been in a long term relationship with her and were talking marriage and kids, nor did you sleep with her. It's a date and the point is to see if you are compatible and if can develop into something deeper. If you know off the bat that won't happen it's a huge waste of time. You're basically going on the date to tell her you're not interested. That just becomes awkward. You'll be wondering the whole time when you should do it etc. I would cancel before the date to avoid that kind of situation. Don't worry she'll bounce back and find someone who is okay with her extra package. It's just not you and that's cool. It's actually refreshing to see a man handling this in such an adult and mature way instead of running away from the situation so kudos to you.