OK, this is a difficult one. Can you call again to see if BA have found availability overnight? The FLL alternative maybe for your own account otherwise, you have to give BA a good chance of replacing the cancelled service. If you took the VS service you would get a refund on the BA service, and if you can demonstrate you gave BA a good chance to rebook you then any financial loss may, may, may be claimable. Make a note immediately after the call about who you spoke to, ask which Contact Centre you are using, and get them to put notes on the PNR. In particular, the fact you are heading for a cruise (give them the cruise details). You should also be talking to your insurers, and looking on the internet for alternative business class travel. I can see plenty of availability on United and Delta for example. I can also see some availability on AA, so call that contact centre.

EDIT: There is also a connection via YUL I can see with Air Canada

If you have made every endeavour to get rebooked and BA isn't playing ball then you are in a better place than relying on one phone call.

The other option is to go to LHR and see if they will rebook you on to an alternative service. If you explain about the cruise then they may be more helpful too.