Hmmm OK, we have some conflicting views. Pestilence, it scares me what you say about "the wall", as I fear you may be right....
Think of "The Wall" in front of you. It's endgame here and there are two paths...you move in one direction together, or you split up and go your opposite ways. There's usually no going through as in these kind of situations both parties are very, VERY rarely happy with the outcome.
As I said, you really need to discuss this with her, reasonably. Don't argue. Discuss. Let her know how you feel, and let her tell you how she feels. If there's no convincing her to let you do it and even a compromise, for example that you'll get into it for 6 months or a year and then it's done - just something you want to experience - is still a no-go, then you have a very tough decision to make.
I do believe in that situation if you went ahead and did it anyway, her vision of you will be dramatically affected in the negative - this could lead to deterioration or even the abrupt end of your relationship - she'll feel like you simply don't care about her enough over getting your own jollies. Then again, maybe she won't - she might be hurt, but get over it, and after you've had your fill of BASEing you can stop and say "I'm still here", and that's it.
The future of the relationship is in both your hands, but ultimately the decision is yours. However she feels about it, it's whether you go BASEing or not that will determine the outcome. Life really does suck sometimes.