lovesista, I love your thinking here! 
Yes, you are on the right track, and here is how you should structure this. There is no reason to go into long term debt and pay a lot of interest strictly for FICO. Make the best financial decisions and FICO will follow.
Borrow the full purchase price, minus TTL (if you can qualify for that amount). The point is, go for the largest loan you can qualify for with the best rate. If you need to put $2-5k down in order to get your APR down, then do so.
For this example, I am going to say you borrow $35k on 60 month terms at 6% APR. This would give you a monthly payment of approximately $677.
When your first payment is due, pay $26,500, leaving $8,500 balance. In the future, each month just pay the normal fixed payment of $676.65. However, because your balance is so low, the amount of interest you pay will be only $42.50 the first month and will be less each month as you make your payments. This will pay out in about 1 year. While 24 months is often cited as the best amount of age or history, I believe that 12 months of payments is adequate, combined with a PAID auto loan.
Also, I believe that a PAID $35k auto loan with 12 months of payments history is superior to a LO review than a $2-10k loan paid in 1-2 years. You have shown that you obtained a relatively large loan and paid it substantially ahead of schedule WITHOUT refinancing. This "implies" substantial income discretion and low debt to income and available resources, potentially.
Also, because you immediately (30 days) pay down your loan to under 50% of original loan balance, you will gain a little FICO benefit to offset some of the hit for a new account and credit inquiry.