Wound you do a 30 year or shorter for something like this?

@Ross Yeager there are commercial lenders that have shorter seasoning periods.

HELOCS often have shorter amortization periods (7, 10, 15 years, etc), and can have a balloon payment at the end of some shorter period. 

Modern, direct vented, natural gas and propane furnaces are typically in the range of 92 - 95% efficient.Your decision on whether to replace the furnace will depend on the efficiency of the current unit and whether it make more business sense to replace the furnace or to add a heat-pump with an exchanger insert to the existing system ... and, it is (or should be) primarily a mathematical decision yielding which ever approach is going to offer the shorter payback and lower operating costs.The math aside, there will be other non-math factors.  

If the lease agreement allows for a longer or shorter time period for the Notice to Quit, that time period must be followed.

Your original ask from a lender needs to be shorter. 

We're looking for an attorney that can help us sort out whether we would be limited to monthly rentals or if we could possibly do shorter, AirBnB-type rentals in some or all of the units.

You could go with a commercial lender, but you'd most likely be looking at higher rates and fees, and shorter terms.

The repayment will be a shorter schedule than your mortgage payment.  

Line up a tenant to rent your current house now on a short(er) term basis, like 4-6 months, and if you can get 125% of your PITI payment.