Your vehicle size is too large for the HOV. You will definitely get a very expensive ticket. Both for having an oversized vehicle and for towing a trailer (the toad or anything towed counts as a trailer) in the HOV.
I-10 is the least distance. Traffic delays can happen anywhere. I listen to a Houston traffic channel when I’m going thru the city and will only choose to go north or south loops if the reports indicate a significant time advantage.
But at least half the time that I choose an alternate, that develops a delay.
I also have two advantages you do not. I have a tag and a discount for the Houston toll roads which makes it much cheaper than it would cost you. And I am familiar with Houston freeways that I recognize the locations of traffic delays, and know where most of the ‘normal ‘ backups occur.
Highly recommend just straight through on I-10.