Hey Sean - I'm a Clem owner and Shotgun (seat) super-fan, too! (and super-envious of the new yellow ones, congrats!)
I couldn't find any way to make it work on my Clem. I think the biggest issue is that there isn't nearly as much clearance between the frame & fork on a rigid Riv as there would be on a full-suspension MTB (for foot clearance). The 'top-tube' is also too steep to allow for a level saddle position. I've ended up keeping my FS MTB operational specifically for riding my son around on the Shotgun - it's easily the most fun parent/kid riding experience we've had, and I think it more than justifies keeping an extra bike around just to make that possible!
Another note on the Clem* with kids is that I've encountered a lot (like a lot, a lot) of flex when using a rear rack-mounted child seat - It's workable on simple paved-surface rides, but I would never want to use a setup like that off-pavement.
*1) my Clem is a huge 64cm, 2) my rack is fairly cheap (but has a 50lb weight limit) 3) my seat is a Burly, which....isn't particularly -- all to say that the Clem is likely only a part of the flex-inducing equation
I would also love to hear from any other parents who have figured out how to replicate a Shotgun-style seating position on a Clem or any other Riv for that matter - that would be amazing if possible!
Nick