What a wonderful opportunity for a lifetime cruise and to get to know your boat in the relative comfort and safety of the ICW! I get excited just thinking about it.
Seeing as how you're presumably new to trawlering, I'd suggest the GICW to Ft Myers, across the Okeechobee Waterway, then up the AICW. If you're comfortable enough then for an offshore jaunt, run outside to NYC, then up the Hudson to Albany and over to Oswego. I've covered all those miles and it can be a relaxing trip with proper planning. There's a lot to learn about locks, bridges, anchoring etc. but that's 1/2 the fun.
No one has mentioned the inland route...not sure if it's still open?
Like others have noted - a good rule of thumb is to plan about 75 miles per day and be prepared to cut it short or go longer. The only time we tie up to anything is to buy fuel, get stores, pumpout or lock thru - we never stay at Marinas.
for valuable firsthand information.
Oh, and get yourself an unlimited towing policy before you head out.