Andy,
While you don't want to play them, if you want to tour the Oaks, Panther Trail, The TPC, the Palmer's 27 holes, or the Player course let me know. I have no easy entre' to Carlton Woods and have only played it once since it opened, but you're not really missing a lot there other than the clubhouse.
I concur that if Blaketree National was available Mondays you'd really have to go for it.. The Cypresswood Tradition is stressed but still worth a look, Elkington's Fish Creek's old back 9 and newer 9 are much fun, as is Ogrin's High Meadow Ranch with 3, 6-hole loops.. you could do those both as they're relatively close, but might mentally strain to get your flight by fighting rush hour traffic gioing south through downtown.
I'd take off work in a heartbeat to get on Champions after walking it several times during Tour Championships. Never played it.
I've played a lot at Magnolia Creek and Timber Creek and prefer the greens at the former and setting at the latter.. not sure how much those courses really "embody the spirit of gca," (Magnolia is all artificially pushed up and quite hyped) but they're certainly fun and timewise unbeatable as they'll let you get to Hobby very quickly in PM.
Perhaps a warmup at the front 9 at Memorial Park followed by 18-27 at Magnolia would be sufficient exposure to mid 80's temps and humidity.. the 5-6-7 stretch at Memorial is great bunch of holes..