I can't help much from the birding aspect, but do live a 30 miles north of Clearwater. A few suggestions.
1) Fort DeSoto park is at southern end of St Pete and I believe is known for some birds
2) Tampa Bay is known for beautiful sunsets, maybe catch a bird on one of the piers at a beach with sunset behind it.
3) Tarpon Springs is a very pretty little town 20 miles north, largest Greek community outside of Greece, they do boating excursions but probably mainly aimed at fishing.
4) Florida aquarium (and others) offer boat rides aimed at seeing dolphins.
5) Don't drive all the way to Sanibel/Captiva, plenty of nice beaches in Tampa area. One of the islands Egmont key is only accessible by ferry from Fort DeSoto. Similarly Caldesi is only accessible by ferry from Honeymoon island.
6) Weeki Wachee is about 50 miles north of Clearwater, has a famous underwater mermaid show, but also there is a boat trip down the river, might see some wildlife there also.
7) Silver Springs near Ocala, 120 miles north is an older park, no Disney stuff there. Large area to walk in, parkland etc. There is a glass bottom boat ride in the springs, underwater scenes from several movies were shot here.