The loan remained in her name since the property was purchased and even after she was removed from the LLC.

@Khandbari Rai pros- you can make a  smaller  payment ( the Int ony  payment ) for  up to 10 yrs    ...cons - the rate for this program is slightly higher than regular amortizing loan ...if you make the min payment - your loan balance  will not move  down at all  over  10 yrs  -  the lender  uses the  full amortizing  payment for qualifying  ...at the end of 10 yrs - the lender will change the payment to a  fully amortizing payment for the  remaining balance over the  remainder of the loan term ( likely to be 20 yrs)

The purchase price is about $350k, but the assumable mortgage only has about $250k remaining.

To use our remaining VA entitlement and put down as little as possible (without paying PMI), and quoted 5.375% interest by Meritage's preferred lender, our estimated cash to close is $72,000. 

I wouldn't necessarily go for 15% down, but if that allows you to use the remaining capital to out preform the cost of the higher rate, then I get it. 

I see that property prices remain relatively high but there is some softening.

Remaining principal $300k. 

Our rentals have remained rented this entire time, and we are still at 100% rent collection on time every month. 

For example, if they're going to be able to cover 75% of the entire value of the next property, they should have a much easier time getting approved for the remaining 25%... depending on what kind of asset the new property is.

Inventory remains low but you can find a deal if you stay consistent with your search and get aggressive when opportunities arise.All the best!