We were down in Big Bend a couple of years ago. It was awesome, and definitely on the do again list. There will be a large variation in temperature between the desert and the Chisos basin. When we were there in early June, desert was 70-100F, basin was 40-80F. I would plan on cold nights in the basin in October ! More weather data-
https://www.nps.gov/bibe/planyourvisit/weather.htm
We were driving my Ford Expedition (2004 NBX, a rarer model offered for a few years with a real 4x4 drive and suspension). We did a bunch of the improved dirt roads and a few sections of the primitive roads. Clearance and traction wasn't an issue, but (even on the improved roads) width and turning radius was a problem. I still have the big scratches down one side from the upslope Mesquite trees, from avoiding a minor washout on the downslope side of one of the "improved" roads. The full width sections were just barely wide enough for the Ford. I decided I was really glad I wasn't trying to drag the M35A2 through a bunch of the places. A jeep, or maybe even a M1009 would be way more fun on most of the roads in the park.
There will also be a couple of Homeland Security checkpoints on the way down, make sure all your paperwork is in order!
I am going to add this to my calendar, but I probably won't be able to make it. Looking forward to the pictures, videos, and reports !