I agree with you about the writing but I have a nearly opposite prediction.

I notice that in all the Harry talking to himself or reflecting quietly chapters he allways thinks something along the lines of "there seems to be almost no limit in what you could accomplish with magic if you really understood it". Several times his mind circles around the becomus godus spell and considers some avenue and decides it wouldn't work for some reason or another. In each case after thinking that his mind goes off on some other tangent.

So my prediction is that Harry has his situation get worse and worse until he can do nothing but think about how to et out of it. And while thinking and being forced not to divert his mind to other matters he will review clues that were allready available to us (had we been paying closer attention) and by reviewing the right facts in the right order he will deduce something about how magic works. That deduction will allow him to cast some absurdly powerful spell that solves his problems.