Jon, obviously you're hittin' the real biggies and will be doin' lots of travelin'. Each to his own. Based on my three trips from the USA to play golf in Scotland, my strong preference would be to stay one place, or two at the most, and play what you can in those areas. Troon would be one base (where we spent 8 days on a one-base trip in 2004) and St. Andrews would be the obvious other. I look at your approach as putting notches on your sticks, which is just fine, if you think that is really what you want to do.
In any case, I hope you have a great trip.