Trying to go into an existing template and add/change variables is very tough.

Some other loan type that would not interfere with the projected ROI would be ideal but not sure if they exist, any thoughts?

Does not exist. 

If you have a high return on equity, then you are more likely to be making high revenue relative to your existing payment, which means you would be more able to cover the higher payment of a cash out refi and would then have cash to deploy. 

This is not a rescue type situation nor a new development type situation but rather an existing high occupancy project, but why can't a sponsor raise enough common equity?

@Wiley Strahan..there is a gap for this type of financing, but it doesn't mean it doesn't exist. 

Taking over the property subject-to (Subto) the existing mortgage is an advanced tactic and can be highly effective when cash flow or equity potential is strong.

Contacting other drywallers in the area to provide estimates to complete and remediate the existing job.

You are probably looking up seller finance and sub to and ignoring getting the best tenants into your existing property or finding ways to upgrade the cash flow.

More importantly, every municipality that allowed for Airbnb investment properties and then switched and banned them also grandfathered in existing licenses.