I couldn’t find this on search, but driving down from Punta Gorda and staying at Caribbean Beach. Our first park is AK. Can we drive right to AK and park there without an extra charge if we show we have hotel reservations?
Yes, the only real catch - in my experience - is the FL heat. The heat can impact a variety of items, not just food. It can be a problem for many medications, and cosmetics, for example.
A travel cooler bag can help for some time. I can't tell form your post if you live in Punta Gorda, or you are vacationing there. If you are vacationing, some places have full size fridges and some, like WDW, only have small dorm fridges. Some small dorm cubes have a freezer, but many don't. Some hotels will freeze your cold packs, some won't.
A little trick I have learned is to sub cold, un-opened soda cans. Mind, they won't keep food to safe temps, but if you just want to keep non-foods for getting over 80 degrees, cold soda cans work for some time, maybe half a day? (that's actually sometimes our strategy, hit rope drop, then go to our room mid-day when crowds are at their peak.
You can do online check-in AND you CAN actually check-in at the hotel that early. Sometimes our room has been ready at 7am, other times it wasn't. Either way, you can always leave some or all of your bags with bell services. then they will be kept in air-conditioning. They can also store items (food, meds) in a real fridge for you.
Somehow we always end up with chocolate at WDW. So we end up taking it to bell services to be kept cold. Bell services will also hold your luggage on departure day.
Almost always, if you are going to AK, it will be faster to drive to the park than taking WDW's free transportation, if you do opt to go by the hotel before the park. Of course you'll arrive even faster if you go directly to the parking lot. If you are arriving very early you are also very likely to get a great of very good parking spot. I don't think the trams are running, but it is usually a pretty short walk to the park.
One last thought is that rush hour traffic can be a factor in the Orlando area. Maybe use a traffic planner to get a sense of how much traffic normally impacts traffic on your route, and pay extra attention that morning if arriving early is important/feasible. Also, in the before times, WDW often had speed traps!