If I were Monahan i'd sign with a contender instead of a team that will trade me if I play well. that's just me tho

Perhaps but some of the legit contenders might not have the cap room to take a flier on Monahan with the risk he misses half the season injured. He could ensure his 3 million by signing with the Habs

He'll have to decide between top 6 minutes on a poor team in an attempt to raise his value, or bottom 6 minutes on a contender where his value may decline further.
Of course he could find a contender with a weakness at center and play himself into the top 6, but chances are nobody is going to go into next season with him earmarked as their 2C, so he'd still have to play himself into that position.

Signing with Montreal (or similar) can put him in a position to both earn a better contract and have a shot at the playoffs via trade.

Either way his priority has to be a healthy season where he doesn't miss significant time. Not sure I'd bet on that happening with Montreal. I still say there has to be something wrong internally to have that many significant injuries occurring that frequently. Maybe incompetence in diagnosing injuries or something inane like not enough milk in their diets.

Personally I'd rather have control of where I play unless montreal gave a NTC