Is there a way to sell a property across two tax years instead of one? 

What the other two gentleman said. 

I’ve also considered a 203k loan for whichever asset class I’m able to get the numbers to work with, and over the year or two I live in it, I’d continue adding to my savings and building equity so I can use that to put down on another property afterwards.

I have received 3 quotes from general contractors at two of them came in at around $17k without trade repairs included (electrical, plumbing, and HVAC).

Two drastically different markets and valuations.

Two units are occupied, will need to pay them to move out.

Adult roommates cohabitating on my block tend to live 2 per building and keep the third bedroom, which is small, as an office or guest room. 

If this were my first, second, or third deal I would calculate that expense in to be "safe"; or if it needed repairs, but no.

Did they have a third party inspection that showed the mold inside the property was different than the normal airborne mold?

If it does, then you're almost certainly qualified, and your third stop will be a QI - qualified intermediary.