I am so sorry to hear about the struggle you have to go through just to get onboard. Sorry that I don't have any answers but I don't see how Carnival can stop you from going on a cruise you have already paid for.
They will want to charge the gratuities to your onboard account at the end of the cruise. That will come to about $10 per person per day. I guess you will just have to explain about the direct deposit when you check in.
I am not for anybody "stiffing" their onboard crewmembers, but if it means the difference between you having the cruise you paid for and not being able to go, then I would certainly make an exception for you. It sounds like you really deserve a vacation with all the troubles you have encountered.
Please let us know how it turns out.