Geoffrey,
You should try concentrating on one coast, east or west. I'm not sure how many days you'll be in Scotland but it might be a waste of time to drive from coast to coast playing St. Andrews one day and then playing Prestwick the next. If there is a must play course on your original list ie TOC, then I would recommend staying in St. Andrews and focusing on the courses in that region. Also, if you're flying into Edinburgh, North Berwick, Muirfield and Gullane are in close proximity. From there you can head to St. Andrews where you have TOC, New, Jubilee, Castle, Kingbarns, Crail and Carnoustie and a host of others close by.