Since you do want the help to your scores by improving your credit mix, that's what I'd do. You probably ought to run it by your lender, explaining what you're up to, to make sure that it will be OK, and maybe to let them know that you're not a lunatic of some variety.

(They should be aware enough of FICO scoring that they will understand what you are doing, and approve.)
If you can get that first big payment, or at least 51% of the balance, paid before the statement date, you can avoid an initial score ding for high installment util. Even if you can't, though, it will go away when your account updates again.
Loans, including mortgages, seem to update a good month behind revolving, so it might be a while before you see anything much happening on your reports.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007