There was a natural barrier of investing time into writing the proposal.
This barrier is clearly broken now.
A different barrier could be money that people submitting grant proposals would need to pay. First grant proposal could be $0, second $1, third $10, fourth $100, etc.
Or more limited in impact — flag people who are behaving outside of the norms for manaul review, i.e. too many or too frequent submissions. Manual review and if any are found to contain AI, assume all are AI, and charge only that person a fixed proposal review fee going forward.
The "if found to contain AI" part will possibly become harder and harder to detect over time, at which point you have to assume all entries could be AI, and flagging or making them pay a review fee would become the standard.
But it's similar to emails, under water your e-mail account has a 'trust score' based on previous behaviour, domain, etc. It could also come from the other side, if a scientist is attached to a university or other research body, they should sign off on a declaration that AI was not used (or used but clearly marked as such), with a big fine and reputation damage for the university if their researchers violate it.
That would need a clear definition of what "too many" or "too frequent" mean. Every time this definition is changed, you'd need to retroactively apply the change. Changing the "person" would circumvent this.
My idea doesn't involve any of that -- you want to submit 10 proposals? $111,111,111 please.
This barrier is clearly broken now.
A different barrier could be money that people submitting grant proposals would need to pay. First grant proposal could be $0, second $1, third $10, fourth $100, etc.