If you have hills nearby, I'd go 2x and at least 34/34 as your low gear - 32/34 would be better.. Remember that bigger wheels have more circumference to turn over, so you need lower gears for an equivalent speed at the same rpm.
As for the wheels, check out HUNT - for under $400 you can get a pair of X-Wide gravel wheels that are designed for 35+mm tires and are perfect for graveling on rough surfaces.
At some point you have to ask if the complete bike route is worth it vs. piecing together what you want. An R7020 hydro group is pretty cheap, and from there you can pick the finishing kit and wheels that work for you. Coming in under $3.3K should be doable, and with no need to try to resell OEM parts that don't have much value in the used market.
There's also this:
https://www.planetx.co.uk/i/q/CBPXTE...-tempest-r8000
$2399 w R8020 and RX800 rear mech. There's some OEM stuff on it, but still a nice build and plenty of room to make upgrades.