I know that not everybody agrees with me, but I don't like the horizontal dropouts on the Cross Check. You'll think, plenty of room for big tires and fenders, and then you push the envelope just a bit, and you have to deflate the tires to get the wheels on and off. I'd go with the LHT for that reason.Have you had specific problems with a Cross Check or just with horizontal dropouts in general on other frames? My Cross Check has coarse-treaded 700-32 tires and fenders and there's to be enough clearance to almost get your fist between the front of the tire and the fender. I've never had the slightest problem removing the rear wheel.
Mine is a Fuji Touring. Have you tried 37 tires? If you have no problems removing or replacing a wheel with 622x37 tires, I'll withdraw my objection.