Almost every lender will finance a single family for 5% (sometimes lower) if it is owner occupied.

For example, you might be able to pay higher loan origination fees in order to secure a lower long term rate.

If it is worth getting my dti lower, would it be better to reduce debt (and debt payments) or increase income (by purchasing rental property with cash, or something of that nature)?

I would start negotiations with those that seem the most likely to leave at a lower rate in case the tenants begin to talk.Some questions that would help everyone out would be.Current RentTarget Rent# of unitsPurchase PriceCap Rate being purchased atCap Rate you could sell atOf course you may chose to keep that all confidential which is definitely reasonable, but if it is possible to share that info, it might be able to help people kind of get a better picture of things in terms of a dollar amount.Good luck!

If I get rejected, is it worth speaking with the loan officer and seeing if they would be willing to extend me a HELOC for a lower amount than I had initially requested?

Though it is a but odd,  usually  seems tax value is lower than market.Cheers 

I think the smallest bedroom is about 75-80 sq ft. as I have been saying there is economically obsolete  ( many of these older homes that need more work than what they are worth on a resale basis) and functionally ( it appears building the cheapest home to the very minimum UBC code is a prime example.I had a rental up in Kokomo I dealt with that heat was too much in the winter and the tenant said either lower or NO rent or I have to move .

There are some other lower income and high crime areas where you may be able to make money but it’s really tough to make the numbers work.

If this terms make the loan not viable, either look to structure the deal differently (creative financing, lower purchase price, etc.) or pass. 

What I saw from big lenders online was noticeably lower but I don't know how that impacts FHA lending.