If you're using a HELOC for a down payment, or for that matter payment in full, I would think most banks would allow it. 

We recently did a full rehab on our kitchen and considered this exact situation.

Use the credit card and pay it in full monthly.

I think your odds are small, but greatly improved if you approach them with your logic, and as a human. 

Places like South Euclid or Cleveland Heights that require low to medium rehab but no full rehabs.

I imagine this was a full time job for them?

The project will require full interior completion and some exterior work as well.

I'm a full-time musician and a long-time real estate investor (always done it part time),  I've owned a few student rentals, a duplex, a single family and I've always always rented out my basement wherever I've lived.  

The bathroom, which when I got it was non-functioning, went from a full bath to a 3/4 bath.

I get a snotty return text (at least that's how I read it as you can't really read a time in a text) essentially saying they hadn't received the unemployment check yet for the last two weeks of August and since I wouldn't let them make payments and wanted payment in full . . .