Wow, we've gone full swing to traders wanting outright manipulation and market fixing to protect their rates. The solution is quite simple, first, remove FRR. With the number of autolending bots, there's no need for it.

Second, put lend durations on their own books. Have, say, four lend books total, 2 day, 7 day, 14 day, and 30 day. This more accurately reflects how true fixed interest markets work. It would also prevent bid/ask from crossing. Additionally, because the lends are callable (the borrower can end the loan and return the funds at any time) borrowers can automatically take the best rate from any book they want. All the time duration risk lies on the lender and can be reflected in yield curve.