This is an interesting trade.
Schultz has better numbers than Petry offensively over their careers, although Petry has been better the last 2 seasons (pts/gm), which Schultz has missed a good chunk of time in. Also Schultz has a lower Corsi for % than OZ start % in most seasons, while Petry has the opposite, which points towards Schultz not controlling play as well as Petry, although that might be due to partners and forwards they are deployed with, I haven't watched enough of Schultz to be able to make that call. Schultz is younger by over 2 years which is nice, but they have the same cap hit and Petry has an extra year, so even though he is more likely to start declining that extra year is worth something because it isn't a guarantee he will, and the contracts are both short.
Bjugstad is an interesting piece. He is middle 6, with his best putting him closer to 2nd line and his career average pointing towards 3rd line. MTL doesn't really need more bottom 6 forwards, especially at his cap hit (even Byron's is higher than I would like, but he has proven that he brings more to MTL than just on ice production, Bjugstad might not). I would say Bjugstad is about 1.6M overpaid from a trade value stand point, he has value as a 2.5M 3rd line forward with upside and he loses value the higher his cap hit is.
Overall, I think it's a fair enough deal, Petry probably has a bit more value than Schultz right now, and even with his cap hit Bjugstad's upside should make up the difference with a bit of value to spare. Maybe MTL add Hudon who is a year older than Simon or Aston-Reese but has a better career high than them, it would also balance out contract numbers for the 50 man rosters. If this deal, or something along these lines were to happen it would most likely be late in training camp when MTL is sure neither Poehling or Suzuki will make the team, because the main opening for Bjugstad would be on the RW where Suzuki is likely to slot in if he makes it, or where Tatar, Drouin or Domi (shifted back to wing to make room for Poehling) would slot in if KK, Danault and Poehling are the 1-3C to start the season.

MTL says no to a defense downgrade and adding one more bottom 6 player.

if you can wait until the TDL and clear some cap space , Petry will probably be on trading block for a 1st +prospect if no play off for us
we can't trade him yet if we are not sure that Brook can take his spot