Purchasing Home- Questions (seller assist, interest rates)

[Scott Anthony]

Hey all, so in the midst of trying to purchase our first home.  Long story short, we put an offer in on a house that we saw the day it was listed.  We offered asking price with 3.5% assist.  They went with an offer that offered no seller assist.  Today I found out the house is on the market because the buyers backed out.  Now the ball is back in my court.  I'm offering asking price with 2.5% sellers assist and that's pushing my limit.  I can't do much more, as this is at the top of our range.  With that said, here is a question I have about locking into the interest rate.  I am currently bringing my credit card utilization to 30% (it's high now), but I can pay that down this week to 30%.  I know they report to credit bureaus about every 30 days.  With this change in my credit score, I know I would get a better rate.  Now, if my offer is accepted, when is my interest rate locked in?  Can I lock in my rate at closing or just before closing?  Can I make that part of the contingency? I heard something about a floating rate but lock in 10 days prior to closing?  If anyone could shed some advice, that would be great! 

Thank you!