Ha, I thought maybe you were traveling in an A or C.
I don't think a 4X4 truck of any type would have much of an issue getting onto any of the beaches down here. I do it in my 2WD F150 with street tires. I just get a running start before I leave the pavement.
Bring a small shovel and bucket. If by off-chance you do get stuck, dig out the sand in front of all 4 tires to make the sand level with the tire and then wet the sand in front of the tires good to pack it. There's plenty of water to fill the bucket.
Freeport and Brian has tons of driftwood for a campfire. We collect some for landscaping around the house.
You might consider Matagorda Beach as well. It's very popular with the campers and easy on easy off. They charge a small fee (I think $10) for an annual pass but I doubt there is anyone collecting that during off season. There is also a nice RV park there off the beach.
The down-side to all these beaches other than Surfside is there isn't anything close by to stock supplies. Bring what you need with you. You'll pass a Bucee's on your way to Quintana, Freeport and Brian. That's the closest store. Interesting store at that.