You could take HWY 6 South, catch 45 onto Galveston Island and take the ferry across to Bolivar Peninsula, then head back North and pick I-10 back up in Winnie.
I can tell you that I would rather take I-10 than try to navigate my rig through Galveston. But that's largely because I've been to Galveston dozens of times, so it's nothing new to me. And some areas of Galveston can be pretty tight quarters.
It's a considerably longer route that will take considerably more time. But it will definitely be more scenic and interesting!
Other than that, you're looking at a toll road around Houston, punching the gut on I-10, or taking a REALLY long detour. Beltway 8 around S. Houston is DREADFULLY boring, and there are PLENTY of places you DON'T want to get off the freeway. So if you decide to go that route, be sure you're full up on fuel so you don't have to stop on the Belt. The North Belt is a bit more "interesting", but still a major HWY and toll booths to deal with. In my experience, traffic is generally worse on the North side too. Neither way would be worth it IMO to avoid I-10 if you're going straight through. The traffic will likely be at least equally bad, and there are toll booths to contend with.
I still contend that you're best off timing the route to get through Houston at a non-peak time and just ride on through. We've generally had good luck in the late evening. Watch out for construction coming through Rosenberg on 59/69.
-2018 Greyhawk 29MV
-1997 Jeep Wrangler YJ (Toad)
-2015 Jeep Grand Cherokee Limited (Soon to be Toad)
-2014 Jay Flight 28BHBE & Ram 2500 6.4L CC 4x4 (sold)