For a ~300lb load (rider+bike), a wheel needs to be well-made and fairly tough.
I'd suggest going with at least a 36H/36H (front/rear) combination, or possibly a 36H/40H. The spoke lacing pattern can also make a difference in strength.
Some strong wheels include, for example: Velocity Cliffhanger, Velocity Atlas, Sun Rhyno Lite. A larger (wider, greater volume) tire can also help. Say, something like a Velocity Cliffhanger 36H/40H rim, DT Swiss Champion 14g spokes and nipples, with a 700x42 or 700x45 tire. It'll certainly be heavier than your current setup. But, if assembled by a quality wheelbuilder, I doubt it'd be breaking on you anytime soon.
Here are a couple of sites that might provide some ideas about tougher wheels for heavier riders/loads:
https://www.velomine.com/index.php?m...22_700_709_710
Velocity - Atlas 700c Disc Clydesdale Wheelset
https://www.prowheelbuilder.com/velo...t-package.html
My current wheelset: Velocity Cliffhanger 26" 36H/36H, DT Swiss Champion spokes and nipples, White Industries MI5 hubs, ReneHerse Rat Trap Pass 26x2.3" tires. Tough setup. Ridden on rougher urban-area streets with numerous minor defects and potholes. Not a peep since built. Beautiful set, if a bit spendy.
My prior wheelset: Velocity Dyad 26" 36H/36H, DT Swiss Champion spokes and nipples, Shimano Deore XT hubs, Continental Tour Ride tires. Also fairly tough. Ridden on rougher urban-area streets with numerous minor defects and potholes. Never one peep from the things, let alone any breakage, in several years of nearly-daily use.
https://www.velocityusa.com/product/...iff-hanger-622
https://www.velocityusa.com/product/rims/atlas-622
https://www.dtswiss.com/en/component...es/dt-champion
https://www.dtswiss.com/en/component.../dt-alpine-iii
https://www.whiteind.com/mi5
https://www.renehersecycles.com/shop...rat-trap-pass/
https://www.continental-tires.com/bi...tour/ride-tour