I got a complete LHT with the heavier wheels, 36spoke and Alex Adventurer rims. I think the CC comes with 32 and a slightly lighter/narrower Alex rim. Either way the wheels I got on the LHT were true and even tensioned. I used to own a shop and have built a fair number of wheels. IMHO it's always worth having a spare set of wheels. When I got a CC I transfered all the components from the stock LHT over to it. Rode it for awhile with 38t middle chainring, chainguard in outer ring and 11-34 cassette with the stock wheels. Later turned the front into a double with 44/30 chainrings with outer chainguard and narrow cassette, now it's got 34/48 and narrow cassette but I'm thinking of going back to the 44/30 or 44/28. On a triple crank with outer position taken by the chainguard it gives me a "big" ring that can run the entire cassette for 95% of my riding with the inner ring the bailout gear.
One thing I didn't like about the Adventurer rims is the milling on the braking surface, it made it easy for grit to get caught in the pads and dig further in the rims. I sanded the rims down with 320grit to take some of that off. Not sure if the rims on the Cross-Check are similar but for stock wheels on a mid priced bike they're very good.
I had PW build up some Velocity Synergy rims for it but I'm really not that impressed by them. The seam is noticable , the front is unacceptably grabby and after putting the front wheel in a bike rack, only to fall over and put a 1mm wobble in the rim I'm going to rebuild it with a heavier rim, maybe a 719.
If I was in your shoes I'd get a fancy spare rear wheel and just change tires on the front for changes in use/conditions. Rear rims go long before front ones. If you can't have fun, win a race, cross the country or scramble up over a ravine with the stock gear you won't with gear costing five times as much.