10am - 2pm should not be a problem week days or weekend as stated above.
I travel EB & WB thru BR often and it has been my experience that going EB you will experience some traffic coming off the bridge where traffic from I-10 meets I-110. After coming off the bridge stay in the left lane and follow I-10. Unless you are familiar with BR I would not try to go around it, it may take a long time. Bottom line I stay on I-10 regardless of the day or time.
I-12 is not a problem. No rest stops on I-12 unless you go to a WM or other venue.
Safe travels, Bill.
03, Fleetwood Expedition, 39Z
300HP Cummins, 6 Speed Allison
2013, Jeep Wrangler Sport