Re: boat bottomed out 3 times
I actually vote contrary to what ya'll have said; I'm a bit north of you in fort myers but its very common to see me in a canoe/kayak/outboard skiff with a section of pvc pipe. We own a deep draft boat in a notoriously shallow area and while we are tide limited, knowing exactly where I can-and cannot-be affords me much more leeway. While out there, sight land marks, plot locations on a chart, get as much info as possible. Google earth is a godsend, and see if you can find someone with a color plotter(printer for big paper), they can print off full size charts or satellite pictures or whatever.
Also, call Boat US, they are a very good safety net, not just for getting stuck, but also with trailer assist, break down assistance, and just a general good feeling knowing someone has your back. If you do end up needing a tow you will have paid for your membership-boat us is $250/hr+$13/foot, and seatow is $300/hr+$12/foot, if I recall their nonmember prices correctly

If you call for the tow they charge transit time as well, where as if they see you, they only have that time. Members of course are free. A small kicker to run in and out of the canals with the outdrive trimmed up may very well be in order for you, try to get a 4 stroke so you don't have to keep mixed and straight gas onboard.
Finally, I'm not trying to insult your intelligence or wander off topic, but it is worth saying-the 350 is not as easy as your old outboard, you must be religious about fresh water rinsing after use, if it was a local purchase, have a mechanic check the exhaust elbows, they will rust out in only a few seasons if not properly cared for. Keep on top of the zincs as well, outdrives will corrode to nothing in the blink of an eye, this is of course in addition to the bellows and such. Stern drives in this area can be a nightmare maintenance wise if they are not properly looked after.
Sorry about the length, and good luck with whatever you decide to do.