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EHICs do not apply on the ship but would apply ashore were you to be injured ashore (in the EU). Travel insurance should cover you for any medical costs on the ship but you would have to pay it up front (by credit card) and claim it back. It's a US ship ultimately and US medical conditions apply, basically it's private medical care. That said I don't believe RCI are any different from other cruise lines in this respect. Don't go to the doc for anything trivial that you could get from a pharmacy ashore if need be; travel sickness pills are available free from the purser's desk. Your UK electrical items will work on the ship with US adaptors.
Thank you Wilkie for your full and comprehensive answer which is appreciated, Thanks.