Probably a no-go for right now. My whole experience is with side discharge; I've never bagged or mulched. As stated above, the grass throws out better if you're cutting less, and/ or if it's dryer.
On the other hand, something I used to see at my first job (at a hardware store) was high lift mower blades. It seems they're designed to move more air, which would be a benefit for you here. They're made in several styles, but I found you a picture similar to the ones I remember most. (That doesn't mean they're the best, I probably remember them because there were two colors, and my school colors at that.)
The ones I'm thinking of had another piece of metal bolted onto the three holes of the lift section, making it even higher lift, by maybe ¾" or so. That piece happened to be red.
High lift blades can be found online or, I would assume, you can still get them at a good hardware store. There may be some
made for your mower. If they sell a bagger, I'm sure there are. If you're looking at a hardware store, though you can compare what they have to your old blade(s). If it bolts up and the length is right it'll probably work.