“Southbound” (C&C29) successfully carried about
5'-8" (as burdened) throughout the Bahamas (excepting the Abaco’s - which, believe it or not, we never sailed). Although, in this instance,
“Less is more” (Mies Van De Rohe), I don’t think that your 5'-6" draft should present a substantive problem.
As Stede advises, you can play the tides (range about 3 Ft), on those few occasions ,such as the entrance to Norman’s Pond, Current Cut, and perhaps Bimini [ which has been previously discussed

], when you want to cross a bar. Most cuts and passages (and anchorages) will accept up to 8' or better.
Those that recommend “shoal draft” (I'm not refering to anyone in particular - there's lots of them) for the Bahamas, are real “gunkholers” (OMO) - and you should not let their exhortations scare you off; unless you, too, wish to explore "off the path" (we use our dinghy for this).
In my (not so humble) opinion, anything under 6' draft (fully laden) is OK.
Regards,