Light Bicycle can make a rim brake version of many of their rims if you ask them to specifically. I think they use a graphene brake track with a grooved surface. It doesn't come that way by default. This one might work:
RM29C06 Carbon MTB Rim - Light Bicycle
I might do it in the future on this 26" rim when my current rim brake track wears through because I can't find any aluminum rims that I like in 26".
RM26C02 Carbon MTB Rim - Light Bicycle
Underneath in the comments someone asks:
Brent 2019/09/15
Hello, Do you think there is enough interest in making a rim brake version? I would really like some carbon rims for my vintage bike. Thank you
LightBicycle 2019/09/16
Hi Brent, It is okay to manufacture this 26er bike rim with rim brake version. We just sent you quotation through email. Please check. Thanks, Lightbicycle
Here's a road wheel that has the rim brake grooves they use. It's wide enough for you, but heavy and you probably don't need the aero shape:
AR56 Carbon Road/CX Rim - Light Bicycle
Carbon wheel and rim brakes have been use for years for muddy cyclocross. I don't think it's a problem. In my case, I stay out of the mud anyway.
Lots of QR hubs are still available, and also lots of choices for hubs that can convert between QR and thru-axle. Here's a budget hubset with DT star ratchet (non-EXP) compatible parts (54T might not be reliable according to this thread
DT Chinese 240s (ZTTO M1 Boost hubs) | Page 3 | Mountain Bike Reviews Forum (mtbr.com) , but can swap it out for 36T DT units):
ZTTO NEW Ratchet 54T Disc Brake MTB Hub 32H 32 Hole Thru Axle Quick Release XD HG MS Ncleo 142 12 100 135 Sealed Bearing|Bicycle Hubs| - AliExpress