Possible Stuck Fermentation

Less than a week ago I brewed my first all grain recipe. According to my software the OG should have hit at 1.067 (Actual: 1.065) and FG was estimated at 1.017. The fermentation took off rapidly for two days followed by slowing drastically. I checked the gravity when it slowed down and again today (4 days later) and both times I found a gravity of 1.025.

Today, about 5 hours ago I started an experiment that I don't know whether or not it is valid. I hydrated champagne yeast and pitched it into the cylinder I was taking gravity readings off of (roughly 3/4 cup). I put the mixture into a freezer bag with a lot of air and I shook it vigorously to aerate. I then squeezed all the air out of the bag and let it sit. Four hours later there is no CO2 that has accumulated. I took this to mean that there is no more fermentable sugars in the sample, but I'm not certain that this is valid means to say for sure.

The batch is a quite tasty milk stout that I REALLY don't want to give up on, but I also don't want to wake up to 48 exploded beer bottles when the fermentation decides to take off in a couple weeks. Any ideas?

I should mention two things: Being a beginner, I started the mash at 160 F when it was supposed to be 151 F. I quickly brought it down to 156 F where it stayed for the rest of the mash. Also, I'm not overly confident in how well I aerated when I initially pitched, all I did was splashed around on the surface with my paddle for a few minutes, working up a pretty substantial froth.

Thanks in advance for any nuggets of wisdom!

If your mash was too hot, you'll end up with a less fermentable wort, exactly like you seem to have. I don't think you have a stuck fermentation, but a fermentation that is finished. 8 points isn't too far to be off by for your first AG. Leave it on the cake to clean up for a while more, and then bottle. A little extra body in a stout won't be a bad thing.

Mashing at 161 and then cooling to 156 probably created some long chain dextrins which the yeast couldn't break down, raising final gravity if I had to guess man

I was hoping it had something to do with the high temp. Thanks so much for the feedback!