If you are opening the floor for reciprocal feelings jams, and he is not taking that opportunity to talk, then that is Dave's fault and not yours. It's true that you can't really force him to talk about his feelings, but...

[But Jade believes Karkat when he says Dave won't come forth with this on his own. She doesn't know how to balance Dave's needs with Karkat's, not really, but she also knows that it won't do either of their feelings any good to let it fester.]

You need to have a talk about this, somehow. Relationships are about communication! And if Dave is not communicating, then there is a problem. I guess there are a couple of things you could do before you have to try and force him to talk. I could try and gently encourage Dave to talk to you when he feels ready - only if you want me to of course! It might work better than you telling him, since he would not feel immediately trapped in that conversation.

Or you could ask somebody he is talking to for advice. Like Rose? Dirk? I know you said they are biased toward Dave, but if you approach it the right way, then I am sure they would be happy to help you figure out a way to have the conversation you need. Not talking about this isn't good for him either!