If I rent it out for about $100 less than my mortgage payment will the bank give me a loan with proof of a renter paying the majority of the payment?
that is up to whatever lender you apply to. They will use your income, expenses, and other debts and work some magic on their calculators and tell you what they will loan you. No way to even guess from here what they might lend.
don't ignore that if you become a landlord, you need to have insurance designed for a rental. You also will have to maintain the house when it is required. You can't put it off like you could if you lived there. There is also the possibility of having bad tenants that tear up the place or skip on the lease.
There are a lot of possible problems with renting the place out.
as to removing parts of the house;
as you could have read; so far it hasn't been shown that is it likely to be illegal to take out things you added after the loan was secured. If the house is foreclosed on, there is that recourse issue where the lender can still come after you for any losses realized from the auction. Due to that, causing the house to be worth less doesn't make sense, at least if the lender tends to go after such deficiencies. All that would happen is you got to pay them more because of what you took. Doesn't make a lot of sense to me.
Personally, if you can get out with the $7500 loss you spoke of, that might be the smarted move. You don't have any commitments to a house 2 hours away. You don't have to deal with a hit on your credit report. You don't have to deal with the concern of holding that mortgage affecting your qualifications for a construction loan.