What if instead, you tried this:
1. Sell original home. Deposit sale proceeds in checking account.
2. Refi the full $109K to PenFed's 5/5 ARM with no closing costs. It has a 30 year amortization, but (you'll see below), you'll end up paying it off in less than 15 years anyway.
3. After the refi closes, use the proceeds from the sale of the original house to pay down your mortgage.
Now, under this scenario, refinancing to a 15 year loan on $109K may make the minimum payments higher than you feel comfortable with. I'm seeing rates for a loan of that size in the range of around 3% to 3.125% with no closing costs, which would make your minimum P&I around $750/month.
A 5/5 ARM with PenFed on $109,000, starting at 2.5% with no closing costs, would have a minimum P&I of $430/month.
But if you immediately pay down the $109,000 to $50,000, paying the $430/month for the life of the loan will have the loan paid off in less than 15 years. Assuming you stick to payments of $430/month, if your rate stays at 2.5% for the life of the loan, it'll be paid off in 133 months (11 years, 1 month). If rates jump up to the max, it will take you 138 months (11 years, 6 months) to pay off the loan. If you maintain a $430/month payment (which will be higher than the minimum payment after the first 5 years), and your rates jump to the max each time, your average, dollar-weighted interest rate will be about 3.125%. So this approach will not cost you any more than you would pay for a 15-year refi of the $109K balance, will probably cost you less, and gives you some flexibility.
Don't assume I know what I'm talking about.