VP ellipsis gone wrong

I've posted about VP ellipsis before, which is where we leave out the verb phrase in a series of wider phrases when it can be recovered from context (or in fact from any context). Wikipedia supplies the example of I always tell Mary to do the dishes, but she never does, where the elliptical phrase is "do the dishes", i.e., she never does [do the dishes]. The type of example I'm specifically referring to is something like I can and will pass this exam, where we have two coordinated IP's headed by can and will, and the VP is left out of the first for the sake of not being redundant. It would sound strange to say I can pass this exam and I will pass this exam.

Sometimes this can go rather wrong, as it did on one of the recent applications I was filling out for Ph.D. programs. The question was asking what outside fellowships I had applied to, or was planning on applying to. The exact wording was "fellowships you have or will apply to". The reason this fails is because the VP's in this case aren't the same: have applied to vs. will apply to. So normally we would be hesitant to leave out the full VP's, because otherwise the immediate interpretation is "have apply to or will apply to" which is thoroughly ungrammatical. Of course the meaning can be recovered, but it's still quite odd.