After looking at the map, here is an option I came up with. It eliminates the walking to the starting hole but would still require a shuttle system (dont see a way around that, unfortunately).
Hole # Course hole Hole # Course hole Hole # Course hole
1 Beaver 8 (to 10's basket ) 10 Beaver 4 19 Blackthorn 13
2 Beaver 11 11 Blackthorn 1 20 Blackthorn 9
3 Beaver 13 12 Blackthorn 15 21 Woodhenge 11
4 Beaver 15 13 Blackthorn 16 22 Woodhenge 12
5 Beaver 17 14 Blackthorn 17 23 Woodhenge 13
6 Beaver 18 15 Blackthorn 18 24 Woodhenge 15
7 Beaver 1 16 Beaver 5 25 Woodhenge 16
8 Beaver 2 17 Beaver 6 26 Woodhenge 17
9 Beaver 3 18 Beaver 7 27 Woodhenge 18
You could also take out Beaver 6&7 and insert Blackthorn 10 (after #9) and Woodhenge 14 (after #13) instead. That would be a longer walk between Beaver 5/Blackthorn 13 without playing, but would give more balance on the courses (13/7/7 vs. 11/8/8). Just a thought. I gotta get out and attempt Shoreline!!!!