Great questions. Just so that folks can help you best here, can you clarify a few things for us? You wrote:
Undergrad and grad loans total to 45k. My two loans from grad is about 24k and the the 6 loans I have left for undergrad is roughly 19k (I paid off 4 already).
(1) I am assuming that these numbers refer to the amounts you currently owe, rather than the original amounts that the loans were for. Is that right?
(2) If it is the amount you currently owe, can you also tell us what the amounts the loans were for as well? (A total figure is fine.) I am just curious to see what your installment utilization is.
(3) You mention that the total is 45, but you break that down into 24 and 19. But 24 + 19 = 43. Is one of those numbers a typo?
(4) Are all of those loans at the same interest rate?
You might want to talk to some LO's from a few other lenders, just to see if they all have the same set of DTI concerns. (And make sure they all understand that you are in a loan forgiveness program.) If so, I'd just talk to them about whether they have a preference about what they want to you to do (pay off one big loan, pay off several smaller loans, etc.). The "person" you are trying to make happy is the lender, not FICO. FICO does not care about your DTI, and paying off your loans will not make your FICO score higher. (indeed, when a person pays off a loan that is close to being already paid off, it can lower his score, but I doubt that's the case for you.)
PS. One more thing to consider is whether you are sure you want to buy a house. If you really are in a program that is committed to paying off all 45k of your SL debt (the forgiveness program), it may be worth thinking again before you cough up your own money to pay off any of that The cost of that is quite high, when you consider the long range implications of what you could have used that money for -- e.g. putting into a Roth IRA, etc.
OK. I still encourage you to sit down with another person who you trust and, as you say, do the math. Work through all pros and cons. Stuff like whether you plan to live in the house you biuy for a long time (many years) -- if you do then that is a point in favor of buying. There's also the cost of repairs, insurance, etc. etc.
But let's assume that you decide there's a strong ultimate advantage in buying (even if you lose, say, 20k in paying loans you would not need to if you rented). Then I'd go by what I said earlier. Run your situation by a number of mortgage lenders. If they all say that they need you to pay off a lot of your loans, then it sounds like your desire to own means you will need to do that. Ask the lenders for the details of what they want you to do.