I know there are some DSCR type of construction loans that don't factor in DTI.

Find an agent that can help you find properties that you're looking for, they should introduce you to a lender that can get you pre-approved for a loan, if you can/learn to manage the property or get introduced to property managers, always ask about different contractors that you can use for different things like electric, plumbing, HVAC, kitchen/bathroom remodels.

https://themortgageshop.net/in...I don't see anything on their site about STR loans... 

That is the standard list of documents required by all banks if you are using a traditional loan. 

I'd recommend talking to a mortgage broker that specializes in non-QM loans including "2nd Home" vacation loans

I secured a 250k physician loan (no money down) at 7%, which brings payments to 1707/month, and 1887 with insurance and taxes.

How do you increase the loan amount from 320k to 382k? 

I did a pretty conclusive poll of about 14 lenders of all sorts and each and every one wouldn't allow larger loans for operating STRs.

Conventional loan.

Market is still affordable to get into and cashflow is actually still possible even with high loan to value properties.