Other than paying for an appraisal or BPO (and maybe a credit report), you should not pay a lender anything until your loan funds.

The two existing LTR units (on my family’s property) were built 5–8 years ago at a cost of about $80,000 per unit, so I’m estimating a 20% increase in costs for the new builds.My plan is to use the equity in the land as the down payment for the construction loan, which I expect will make closing costs the primary upfront expense.

For active investments I advocate considering how you can diversify WITHOUT ceding your competitive advantage nor the superior profitability of the niche your in.As an example my business is running an investment fund and syndication high interest commercial mortgage loans secured by income producing real estate. 

I was told by Wagner that the builder is trying to refinance the construction loan as the cost of construction has increased. 

So there are a million realtors, loan originators, accountants (RE is, for most, not complex vs other small business.)

At the current scenario, without knowing anything about you or your properties I will recommend either to look at a loan from your assets using DSCR loan.

The current lender refuses to do a loan assumption. 

And if it were set up where everything went through a title company so the buyer pays the title company, they manage the buyer's loan (from me), and the title company ensures my mortgage is paid without my direct involvement... what parts of the transaction would feel risky or not worth the headache to you? 

Most non-FHA loans will require at least 15% down but you'll have to have amazing credit.

I would upgrade properties every 12-15 months as allowed by low down payment loans if my significant other wasn’t risk adverse and opposed to moving.