I think this is something better suited to the solo golf traveler, unless people agree on a course and are committed to seeing the process through or have a plan B if something isn't working. I also think that this type of trip is better suited for a return trip to a a course that has an appeal you want to explore more.
I did a variation of this type of trip last summer, with a five round in seven day ticket at St. Enodoc, followed by five rounds that included two at Saunton East, one at Saunton West, one at Royal North Devon, and one at Burnham and Berrow. I wanted to try something different and did not want to take on a lot of driving. I picked St, Enodoc due to being one that sounded most interesting from the Confidential Guide and one that seemed realistic in terms of access and affordability. I got a nice email back from the club that was encouraging, so I planned the trip many months in advance and got a good airfare to London and hopped a train to Exeter for a night of sleep and picked up a car the next morning. It worked out well and I would do it again, most likely focusing on a single course I had played before or one in an area where I had other options.
A few years ago, I spent a week at Barnbougle after both courses were open. I had previously spent three days at Barnbougle Dunes in 2008 when the Lost Farm was being built. Both trips were part of multi-destination trips to Australia.
In the past few years, I have traveled and mostly played at clubs where I have a membership but one has two 18 hole courses and one has four 18 hole courses. I think of this as different from what this thread is discussing.
I have done over 30 overseas golf trips that included over 160 different courses outside of North America. Many were return trips and the pattern over time involve breadth on earlier trips and depth later. Even on earlier trips, I often attempted to play multiple rounds on some courses and book extended stays in some areas., so I might have played 22 rounds on 18 different courses or 27 rounds on 23 different courses.
I asked the question about courses in England that would be both accessible and affordable, given that I have periodically gotten emails from courses I have written to that are basically not available for play during several day time windows, even when writing many months in advance.
Charles Lund