You still need rigorous proofs at the end, if you are trying anything new. I think I would look at it more as you might try an ugly/practical approximation, or

You still need rigorous proofs at the end, if you are trying anything new. I think I would look at it more as you might try an ugly/practical approximation, or add a term, or whatever just to see if it will improve things. And maybe it gets you "close enough" for the application. But if you have a deep think about where you are stuck and come up with a new tool, then you have to be careful.