I had almost the same problem. I finally decided to first submit a paper to
the best journal in my field (did in early June) and to submit a proposal
to NSF in November. Right now I am waiting to hear from the journal editor
and the reviewers. We feel that we can be much more aggressive in the
proposal if the review of the paper is positive.
My team has been busy working on expanding the ideas in the paper. It turns
out that there are many things we can do on top of the paper.