Rising interest rates have hurt everyone’s buying power (except cash buyers obviously), and inventory is locked up because nobody wants to move and give up their historically-low interest rate.

Or, if you were doing the work yourself, bill that hourly rate to the property as well?

That's about the going rate. 

The new loan at a 5% interest rate would then pay off the seller's remaining balance, effectively transitioning your financing without additional down payment.It's also worth noting that some lenders might allow a "cash-out" refinance, where you could potentially take out more than the existing loan balance, given enough equity in the property, which could be used for further investments or improvements.

My preference would be to obtain conventional financing (although this may not be possible) to get the best rate.

I would even obtain a COFI arm permanent loan where the payments were based on an interest rate lower than what the market rates were.

This means the rates are better, but again the process can be a headache.Each loans has it's pros/cons, so it's best to know what your goals are to know which route you should take. 

However, paying off your mortgage that you acquired with low interest makes no sense to most in a 7%+ interest rate environment.  

I own and operate one currently and I'm still able to cashflow with my crazy 7.8% interest rate.

I suspect if interest rates come down as expected this summer that could drive prices back up here.