In addition to Simon's good thoughts:
My research is a number of years old, but at the time, there was no reasonably priced “on-call” services for our size recreational vessels.
We have a friend who is a physician who we asked to be our “Ship’s Surgeon”. He was tickled to be “included” in our wanderings (he is also our phone contact person for EPIRB distress signal). He has our medical histories and knows our medical kit and was willing to take our “emergency” calls (which have “knock-on-wood” in 70,000nm has not occurred). Until recent years when we have had a satphone, he would not have been available (or easily available) when off-shore.
The other go-to item (untested) was:
1. Falmouth Coast Guard, +44 132-631-7575.
a. Using their Medical Advice Link Calls they will connect you to Portsmouth Hospital where there are doctors experienced in medical emergencies at sea.
This should be checked out as this data may be dated.
It may not be smooth or seamless, but SSB calls to US CG vessels can travel a long distance at certain times and conditions.
Let us know what other possibilities you find.
My best, Dick Stevenson, s/v Alchemy