Sanibel has great fishing. That travel time is very optimistic though. Beach traffic on the Causeway can be brutal. Get there very early in the morning or mid-day - if that's not the prime fishing time either due to tides or time of day or whatever, there are some great places to grab food and beer while you wait.
It is a bit out of the way from the direction you plan to travel, but if you go here are two can't-miss spots to try.
Once you're on the island, try renting a kayak from Tarpon Bay and fish Commodore Creek on a moving or high tide. It is lined with mangroves and loaded with small snappers, sheepshead, and the occasional redfish or snook. Even caught a flounder there once.
In the evening, try fishing the culverts on Wildlife Drive in Ding Darling wildlife refuge. The road is one-way and it closes quite a bit before sunset, so check the hours. You need to get through the front gate before it closes. Once you're inside, you can stay until you get kicked out...which in my experience doesn't actually happen. At sunset, the currents coming through the culverts become a fish magnet and it just goes off. Snook, jacks, ladyfish, and baby tarpon will all make an appearance at either of the first two culverts and feed well into darkness. FYI, the wildlife refuge is closed on Fridays.
Heading through Everglades, there are some places along the road you can stop and fish but I've never had much luck there...but I've also had awful post cold front weather every time I've tried to go that direction.