Hi Greg. In paying off your installment loans, IMHO you may loose points as you are reducing the trade mix that FICO likes to see. Types of credit used, accounts for 10% of your FICO scores. I can't comment on student loans, but paying off the car would probably result in a score drop. It did for me, when I did.
You might benefit from getting 2 more cc's. But the immediate impact might be a score drop. But getting some history on them, with perfect pay history and low utils, would raise your scores within 6 months or so.
Are the scores you posted true FICO scores?
The 2 collections are hurting you. Start working to get those deleted from your cr's. In fact, work on those first, before you apply for any additional credit. Those collections alone could get you denials.
It might be a good idea to post the details of the collections so we can help suggest a course of action for you.