I was in both upper and lower Antelope slot canyons of Page, AZ in October (I guess these are the slot canyons you refer too).
In upper, I brought both my 5D3 with 17-40L and my 50D with 24-70L II. I didn't use the 50D, so I brought only the 5D3+17-40L in lower.
From your gear, I'd choose the 16-35L and bring the tripod - especially in lower Antelope. They will give you a 2 hours "ticket" for you to explore the canyon on your own. Consider bringing a remote trigger also for long exposures.
Research how much sun there is at what time of the day in August - the canyons get a very dull brownish look without sunlight. Upper is kinda A-shaped (narrow in the top, wide in the bottom), whereas the lower is V-shaped. This suggests that you should pick Upper during midday, and Lower in either morning/afternoon.
Since you're in Page, AZ, anyway, I'd suggest you consider going to the "Horseshoe Bend
" of the Colorado river on the other side of the town too. This is a sunrise adventure - bring a flashlight.