We have to consider that Hage might not even be willing to consider an AHL tryout contract, and that HE not the Habs control what, if any (theoretically), contract he signs.
The Habs also need to determine exactly what "lower body" injury he has been playing through ... it might be better he not even play again this season and instead focus on training this summer to be prepared to training camp/next season ... signing his ELC, hanging around the team through the playoffs while getting treatment from the Canadiens medical team might be best.
Time will tell