We are soooooo familiar with the drive! We used to live on the I-12 corridor in Louisiana. All my mom's family lives in Pensacola, FL & my dad's family + my parents live in Alabama. We also used to drive to WDW frequently. And I lived in Central Florida for over 10 yrs when I was a kid. In the past we stopped for a night in Pensacola staying with my grandmother before she passed. We also stopped for a night in Tallahassee at a Hampton many years back. Now, crazy as it sounds, we prefer to drive it all the way through. We like to push through, get there, and catch up on rest. Being close for embarkation day is a plus because we get refreshed & recharged in time to start the cruise. Our sons are now 19 & 20 so we have 4 drivers when they come along. Even when it's just the husband & me, we will still switch off a couple times & drive it all the way. We've also driven just the 2 of us from Miami to Houston all at once. We're road-trippers!
We time it so we can get through Baton Rouge when it's not rush hour. That's your biggest obstacle. Their traffic is absolutely obscene. My husband is working just west of Lake Charles, Louisiana now and I can tell you in the afternoon rush hour it will back up at the big bridge on I-10 eastbound. Our current plan for May is to get up & out at about midnight on a Sunday/Monday. Hopefully we'll hit Baton Rouge as rush hour begins. The rest should be a non-issue. We expect to get to the Hampton in Cocoa mid-afternoon Monday. We'll probably force ourselves to stay awake then go to bed at a normal evening hour. I'm sure we'll sleep in on Tuesday to maybe 9. The boys can hit the beach & we'll go to Ron Jon. Relax Tuesday. Solid night sleep Tuesday night. Embark on Wednesday. Normally we don't do a full day with an extra night but we're making that time for our boys to do their sentimental things.
I'm not sure where you're coming from in Texas. For us coming from Houston-ish (Seabrook) I'd say a good halfway spot is Pensacola. We stayed at a hotel right by the airport several years back and it was nice. Good location by the mall. Lots of restaurants. It's also convenient to half a dozen family members' houses so I'm biased on the location. LOL!
The parking structure at the
DCL terminal is secure. I'm more confident with it than anywhere else. We like parking in the structure for the added benefit of being covered in a concrete structure. In the hot months the car won't heat up as much. We always drove our Tahoe which is a bigger vehicle. Never any dings. If it's a concern you can park on the top deck which is most likely to have gap spots. There's also a preferred parking section for a small additional surcharge that seems like the spots may be a tad more generous. When you pull in to enter the terminal area stop by the curb out front where everyone is loading/unloading. You can drop your checked bags with the porters there (give them a little tip

) then go park your car. Then, yes, you just walk over to the terminal building. Not far at all. I think it's on level 3 that there's the elevated walk-across with the dedicated security check. Like at the airport. You'll see it. The preferred parking is a lot on the side of the building so it's even less of a walk. Those spots aren't covered, though.
Let me know if you have more questions.