No way Ottawa does this. Boeser + a 1st for Norris makes more sense, but Ottawa would have to really lack confidence in Norris going forward to do that. Ottawa isn't looking to give up on this season and I don't know how, with the cap going up, keeping Norris isn't in their interest. Sure he's injury prone, and maybe isn't worth 8 mill for what he brings at this exact moment, but if he becomes a consistent 30+ goal scoring center he absolutely will be worth that and more in a couple years.
Boeser + a nice prospect like D-Pettersson and a pick would probably be the package. But as you said, there's no guarantee you use the cap space wisely. Re-sign a 28 year old Boeser at 8x7 instead of keeping a 25 year old Norris for the same price? I don't know if that's the right upside bet for a young team looking to break into the contender class.