There are a bunch of different figures associated with this decision, such as new interest rate, old interest rate, cash flow of new property etc, but I'm having a hard time getting my mind around how to analyze the decision mathematically.  

A good gauge of performance for a full time rental is roughly 10% of valuation (A $1M home should generate $100K+ in gross revenue.) 

Older homes may need updated style, but as long as your rough-ins are intact, everything should be fine. 

Now, you need to figure out how to find deals and pay for them.

Did you figure this out?

So I'd need to figure out an agreement/return between A and B, and then I'd need to figure out an agreement/return between (A&B) and C.

Our goal for the projects we flip and the projects we design for other investors is to figure out how to get the same look at a fraction of the price. 

Bought it as a safe bet thinking it would do roughly $35k annually in short term rents.

Have you figured out any general numbers yet that you'd be willing to share here?

Now, you need to figure out how to find deals and pay for them.