As Jim said, Fort deSoto isn't the kind of place anyone could hide out in for more than a day, as it is dead flat and the parts that are not beach are mostly waterway. I go there often, and there are only 2 places that anyone could hide: inside the fort itself, which might work except that is fully open for tourists to explore around in every day, and in the mangrove cuts, which would be workable only you were only using them to stash a kayak for a getaway; otherwise that's only waterway, so you'd have to hide either in a tree or underwater. The road entrance to Ft. deSoto is gated and there is an admission fee to get in; rangers get very close eyes on your vehicle coming and going. The same goes for Egmont Key, which is flat and has a lot of visitors, but is most notable for what it does NOT have: fresh water.
He's not hiding out in Ft. deSoto; that is, as our UK friends like to say, "a non-starter." What *could* have happened is that the parents left him there to make his own way out on foot, with a stolen bike or kayak, or even on the public bus line, with the intention of having him leave town from Tampa, where he would not be as conspicuous.
There is actually a Puerto Rico theory circulating, which IMO isn't all that way out there as a possibility. If he boarded a plane to Puerto Rico during or just after Labor Day weekend it might have worked, if he used a gift card online to buy a ticket under the assumed name of someone he knows well, and then claimed to have lost his ID. Puerto Rico is a US territory; the domestic ID rules are in effect for flights headed there, which means he could fly without photo ID if he agreed to "enhanced screening" by TSA. If this was the plan, I doubt he would have stayed in PR for more than a hot minute once he arrived, because he would have wanted to get out of easy reach of US law enforcement before the net started to close. Puerto Rico is a notoriously porous segment of the US border, so he could have gone just about anywhere in the Caribbean or even South America by boat from there.
About the phone: the report is that the phone that was purchased is the same phone left behind at his parents' home. It isn't that odd that anyone who had lost a phone might come in to replace it, so that part isn't suspicious at all, as he claimed his phone had been lost/broken on the trip out west. What could be possible is that the realization hit after buying it that a phone purchased at an actual phone store, even if pre-paid, is very traceable, because phone stores keep careful records for marketing. Buying one with cash at Walmart is a whole lot safer if you don't want it traced.