I have no idea what an LCM-6 is but the numbers you mention do give some concern.
If you looK at an absolute range based on gallons per hour it does not really mean you can do 9 knots in all conditions. In heavy seas you might do 4 knots or maybe even less yet burn 10 gallons per hour. Your actual range is perhaps better stated as 60 hours at some moderate rpms. If the weather
is perfectly smooth then you can make 500 miles but not if it isn't. You won't make good 9 knots across the Gulf Stream
either. You will drift north by whatever the current
is as you cross.
Since I assume you would pick your day to cross then your chances of good weather
are far better than just going any time. Obviously what is "better" depends on your own trip plans and how you prefer to clear customs
. Having a fuel
reserve is a better idea so you need to consider that weather can change quickly and predictions could be wrong or you might have problems.
Jacksonville to Nassau
as a straight line is 269 nautcal miles but you would not navigate it that way. The easier way is to head
south first then cross the Gulf Stream
at a more perpendicular angle giving you better fuel economy. Minimizing the time you spend in the Stream seems a good plan. Heading south first would let you fill the fuel tank
before you crossed and save money
since fuel would be cheaper in FL. You really don't have enough range to go over and back from Jacksonville on one tank so you'll need fuel some time.
As I say your own plans may make some alternatives better than others but you need to plan based on the weather. Fuel economy and clearing customs
are also important too. You want to plan the arrival so you enter at a good time of the day.