I don't think I'm going to be much help- here... while i can see that Bus 6 does leave a stop at Stirling and Anglers Ave/Ravenswood Rd and goes north picking up passengers at Tri Rail and eventually into Central Terminal where bus 22 goes out to Sawgrass Mall which is walking distance to the BA center, that is not the routing the BCT website lists - they are showing RT 16, which heads west on Stirling and then a transfer to Bus route 1 heading North on University Dr ( a major north south road here ) and then intersecting with bus route 22 ( I think at Broward Blvd where Bus 22 goes in to Sawgrass ( Buses 22 and 23 both eventually end up at Sawgrass.) I think the routing takes almost 2 hrs. I do not know why they don't offer the route you suggest ( 6 to Cent. Terminal to Bus 23), but it is not given as a routing choice at all on their route planner for your hotel to BA center .
Coming back, Neither route 6 or 16 may be running a sthey show you going to Central terminal by Bus 22 then change to Bus Rt 1 which travels Down US ! south of FLL Airport and would let you off at Stirling and Federal Hwy I believe. They list the trip as taking well over two hours by that route and it leaves Sawgrass Mall at 9:36- so you woud be getting to Central Terminal around 10:30 I think and to US1 and Stirling Rd after midnight. In my opinion I would not want to be at Central Terminal changing buses at that hour , nor would I want to be walking along Stirling Rd from US ! at that hour- i think both would be dangerous, based on the areas and clientele likely to be in those areas late at night I drive through them fairly often by day and have a good idea of the low income areas they are in..
I just don't think it's feasible or prudent for the return trip at all. Just my opinion, but I wouldn't want to do it.
Our bus system is not as well developed as perhaps yours in your city is and the CentralTterminal is not an impressive place and is in avery bad area and I do not know the level of security-Downtown is all but deserted after dark when offices close and there are many vagrants in that area.
It's entirely possible I have missed something as I don't use those bus routes- I am familiar with the #22. and 23 buses both of which go through some pretty dicey areas and Bus 1 is the Bus that goes north and south US1 past the Airport. If you look at a map of that area you will see how far you would have to walk to get back to your hotel after being dropped off from Bus 1. Routes 6 and 16 are not routes I am familiar with except to see via map where they head..
Perhaps you can call BCT when you arrive and discuss the routes with them- but it seems to me not a good idea on the return especially.