"And, I'd bet there are session players that'd be able to replicate Peart's style reasonable effectively"

Replicating Peart's style is hard but not impossible, though many drummers (even great ones such as Mike Portnoy) often get it wrong because they look for speed and perfect timing while the strongest point of Peart has always been his sense of dynamics: he could make a song by hitting only a single drum just by modulating strength of the hits, their speed and time changes.

Jazz musicians are picky about rock drummers invading their lawn (for very good reasons I'd say), but I think Peart made it pretty well. Check this one at the Buddy Rich Memorial Concerts and don't miss the solo, this sounds like a variation of the old solo in the Exit Stage Left live album) I like this one a lot more than the newer ones. https://www.youtube.com/watch?v=T0gYHLkY4qA

To me his very distinctive traits also are his use of upbeats (in fills too) and that famous ride pattern which totally raises attention among Rush fans as soon as you start playing it. These guys nail it well. https://www.youtube.com/watch?v=LRhTmDSrNvE https://www.youtube.com/watch?v=aYaVZojowiQ