Play hooky and just do it. Been keeping an eye on the weather since I'll be in that area next week as well. Looks like it's staying pretty dry for the most part so Monument Ridge Trail shouldn't be an issue.
I have done both of them. They alone are kind of underwhelming. That is not to say not do them. As the journey was worth it for both of them. Monument Ridge has a great view at the top. I have heard that the trail is more of a road now. When I did Monument Ridge, it had rained and it was very muddy.
The other trail Black Trail Wild Bill is a very easy trail too. The views and drive to and from the trail are very nice. Do not expect much for obstacles on this trail either. The ones that are there are man made, like someone with a loader scooped dirt so there was an obstacle. There are some good views in the area.
This was the only spot that needed 4wd. It is a climb from the trail head. The actual BOH trail is in the other direction.
Nice view.
The drive to the trail is worth going. Also since you're in that area, I would look at doing the Road to the Sun in Glacier National Park. It is one of the best roads in the US. I did it years ago on a motorcycle and you would be doing yourself a disservice if you did not try and work that into your trip.