Well I hate to dis-way anyone from making a journey they want to make, but lets consider the following;
Your going to build, outfit and test a boat in 2 months? Do-able but not likely. Why not just buy a Hobie 16 or 18 and find a way to slap an engine
on it and a tent on the tramp? Your going to end up motoring most of the way anyway as the winds tend to be light that time of year and out of the wrong direction if you have my luck.
You will cover 2k+ miles if my calculations are correct (they probably aren't) in call it 100 days (20 miles a day) not un-do-able again, if you have no break downs or want to stop and smell the roses.
You will be traveling at the hottest time of year, and yes, you will be in the mosquito breeding sections of the U.S. the entire time. You will consume enormous amounts of water
which you will only have ready access to at marinas
and will be pricey and weigh the boat to capacity or beyond.
But if it all works out, you can write a book and retire. If not and you become barge food
, you're relatives can write a book and retire! Its all good.