The Disover loan would not help you, since you already have an open mortgage. A mortgage is considered an installment loan.
On the other hand, if you really feel like there is a chance that some model might like seeing that you have both a mortgage and a non-mortgage installment account on your reports (both open) -- and I can't rule out the chance that there might be some benefit in some model -- then I would definitely not go the Discover route. Instead, I would get a $500 Share Secure loan with Alliant. You can find out more about it here (first three posts):
http://ficoforums.myfico.com/t5/Understanding-FICO-Scoring/Adding-an-installment-loan-the-Share-Secu...
The SS loan technique is designed for people with no installment accounts (including mortgages) so don't expect to see the 30 point increase it describes. But using Alliant will save you the hard pull and will get you everything you are looking for in the Discover loan. The Alliant loan will last 5 years and cost $2 per year.
I see that you write:
Credit utilization is zilch since I pay all CC in full.
Two quick thoughts.
(1) You don't want a utilization of 0%, if that it what you meant by zilch. In the 40-day runup to applying for the auto loan, you want all cards to report $0 with one card reporting a small positive balance. That will be considered by FICO to be 1%.
(2) To pay in full means to pay the full amount that appears on the top of the credit card statement in the roughly 25 days after the statement prints. A person can pay in full and still have a high credit card utilization. So the inference you make (I pay in full, therefore my CC utilization is low) does not actually follow. Let us know if it is unclear why that is true and any number of people will be glad to explain.
Final thought: you scores are already plenty high enough to get best rates for auto loans, especially if you apply for no new accounts (except possibly the Alliant loan) during the next year.
