If your STR income doesn't cut it for DTI, look into alternative financing like portfolio or hard money loans.

If not, what alternative strategies would you recommend?

Alternatively, if you're planning on buying multifamily in a low cost of city to get the best bang for your $ - then it might make more sense to do so. 

It is fairly easy to get a loan modification or other alternative to foreclosure (Assuming its Fannie/Freddie, which is still 70% of the market) these days and values are not declining so, its not like we were chasing values down like we were 08-16."

Alternatively, there is space to add a second bedroom.

With so many “alternative” qualifying programs out there, there really has to be something other than “under 2 years employed” or “doesn’t show all his income” for the buyer not to be able to obtain institutional financing, and hence be willing to spend $250k for a $200k house. 

Alternate uses of the same money).

There are far better alternatives. 

Run your deal analyzer as if you are purchasing the house now for $230 and see if it meets your investment criteria (and also compare it to an alternative investment purchase). 

There are alternate money options as well.