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No one will be able to tell you if you will get enough points out of this but I will tell you this; one would want to show him/her self in the best light and with the best possible FICO to a prospective lender.
It certainly can't hurt to let the new util kick in. Have you tried to get pre approved anywhere yet? I know its hard to be patient. My util is NOT good and I still have collections. I got pre approved through Cap One blank check program let the dealer pull as well. Ended up with a rate a little over 5% with 5 charge offs still reporting. All about 5 years old. My scores were a little higher than yours, but I also have 3 or 4 more new trade lines. Do you have previous car credit? This will help if its a positive TL.
Regardless of whether or not you wait, you really want to try and get a pre approval 1st. A dealership is obviously going to try and make as much money on you as they can. This includes making rate. IE. offering you 10% when the bank said 7. If you can't get pre approved, you might want to wait until you can.
A dealership can get you a better rate than you can get on your own. (Not always true of course, but true enough often enough.) It still helps to have a starting point. My Cap One approval was for 7.66% for 72 mos. I ended up with 5.15%.
I was in the business for 5 years, so that helped, but always be as prepared as you can.
And you're never going to know anything without an INQ. 1 more is not going to kill you. i went from 8 to 16 while shopping, but most of those are scored as 1 INQ becaue they were all pulls for a car loan on the same day. Do NOT hop from dealer to dealer and let them all pull.