I'd wait to get the $5K forgiveness since you're so close at this point. Are her parents aware that it will happen? I assume you're worried about this because the loans are in your wife's name, correct? Are both parents writing your wife a check every month and she's paying the loans? How are you certain they are being paid on time?
It sounds like her parents are not a single financial entity for whatever reason (divorce, separate finances, etc.). If her father has means, he might consider it an insult if you go ahead and pay off what he signed up for. If they didn't have an amicable divorce, he might not give his $6K if it means the mother doesn't have to give her $6K. Only you know if that would happen, and if that risk is material to you. While you might think you'd be easing your MIL's burden, she may be insulted too. Ultimately, you're making guesses about what their personal finances are like, and as long as they're making the payments and not voicing a concern about their ability to do so, why rock the boat? Personally, you're going to be related to these folks for a long time, so I'd tread lightly. If you're worried the MIL is going to miss a payment, put her $6K aside until the loan is paid off, and maybe keep it around afterward to help the MIL if she is in dire straits due to her illness.
If the outstanding loan REALLY bothers you, could you make the case that you'd like to start a 529 for your little one's college so you can do for him what your in-laws so generously did for their daughter, but your conservative nature won't let you start until the wife's loans are gone. Say you can't wrap your head around paying interest on one education while trying to save for a future one. Let them know that you plan on paying off the loans after the $5K forgiveness kicks in, and if they'd like to contribute to the 529 plan for whatever they are still on the hook for at that time (over whatever time period they desire, if you'd like to give your MIL a break) you would be very appreciative, but they are under no obligation to do so. At least that way they know the money is going to the family education and not so you can go buy a boat or whatever.
FWIW, I'm also in the "screw the math, pay your house off early" camp. I'm not going balls to the wall every last cent towards the mortgage, but I'm putting a little extra toward it every month so I'm on pace to pay it off a couple of months before I plan to retire. Essentially, if someone handed me a lump sum of cash that was the outstanding amount of my mortgage, I would pay the house off 100 times out of 100, it's just how I'm wired. I hate owing anyone money.