It was a fun thought exercise!
The routings in the old thread that ATB found, while smooth, have a severe lack in par 3s and other factors. The routing I came up with, while a little disjointed and three slightly concerning walks and one rather long walk between green and tee would be necessary, could be a legitimate and interesting test and routing.
Leaving 14 on OC out was a tough choice, but made with two things in mind.
1) For the pros, 14 doesn't play like it should anymore.
2) I knew I wanted to get the Eden hole; 2, 3, and 8 on Eden; and 15 and 16 on Jubilee into the routing. Fitting 14 in would have made things complicated.
One thing I made sure to do... the OC has NO physical changes. Leave her be for the rest of us to enjoy.
Only "connector" hole is 11 on my routing. You might say 5 and 10 are, too, but I think they could be fascinating holes.
ATB, I'm going to repost mine below with a couple modifications after more research. If you want to, you can remove it from the OP to take up less space on the page.
They will no longer tee off from 1 on OC. The first hole is a snoozer. Also, I see the R&A now able to line the left side of 18 with grandstands ($$$).
Hole 1: Par 4. 483 yards. 2 on OC from a tee on 1st fairway on other side of the burn. Gives them chance to surround "1st tee" with grandstands ($$$).
Hole 2: Par 5. 640 yards. 4 on OC played from a tee placed where 1 on NC pinches. Drive up 2 on NC, then they can play up either fairway for lay-up. If there is a gale back into the players faces, using the tees on 2 at NC would still have the hole play about 560 yards.
Hole 3: Par 4. 470 yards. A little bit of a walk from the last hole, but worth it. 2 on Eden from new tee left of barn
Hole 4: Par 4. 450 yards. 3 on Eden. Use tee green-high right
Hole 5: Par 3. 220 yards. 4 on Eden. In this routing, there would be no long par 3 without doing a bit of a reduction. I think this hole would be a perfect opportunity for it. Part of it is to move the tee a bit further away from the previous green. Another is playing this as a 280 yard par 4 would not be interesting in the slightest.
Hole 6: Par 3. 178 yards. 8 on Eden. What a crazy cool hole. It had to be included. Only worry would be the gallery traffic around this hole, but I think it can be done.
Hole 7: Par 4. 455 yards. 13 on OC. There is a crossover in front of the 4th tee (3 on Eden), but it would be manageable, and the walk back to the tee wouldn't be that far. The current Open tee would not be able to be used to give room for hole 4 (3 on Eden); however, the hole would still play as intended. It would require an accurate lay up, and with the entire green now open to be used, Saturday it could be 415-420 yards over the grass bunker in front, and Sunday be 480-490 yards to a hole location on the far/back side of the green.
Hole 8: Par 4. 440 yards. 6 on OC, but now the hole will be located on the far side of the green (#12 normally). The green over there makes the approach far more demanding.
Hole 9. Par 3. 174 yards. A little bit of a walk, but again, worth it. 11 on OC. The Eden hole. Nothing more needs to be said.
Hole 10. Par 5. About 555 yards. A little bit of a walk, again, but nothing too outrageous. Reachable par 5 using 12 on NC from 9 on NC tees. It would make for an interesting slightly-angled right fairway off the tee and the bunkers on 8 at NC could be in play with a block.
Hole 11. Par 3. 162 yards. 13 on NC. Might be one of the weakest holes in the routing, but it will be the shortest par 3 in the routing, and all the par 3s face different directions. A new tee would have to be constructed back and to the right in the area of the gorse to give the previous green some playing space/spectator room.
Hole 12. Par 4. 460 yards. 14 on Jubilee with a new tee a little further back. Lots of places the tee could be placed and not really affect any of the holes currently there. Since the green isn't being shared during the tournament, there would be three very unique lobes that the hole could be cut in.
Hole 13. Par 4. 390 yards. 15 on Jubilee. New back tee located on the front left corner of 5 on Jubilee, or new tee constructed. Very strategic hole. Great amphitheater setting, too, if I remember correctly.
Hole 14. Par 4. 450 yards. 16 on Jubilee. A new tee would need to be constructed, though this new tee might not be possible. If not, even at 430 yards, this would be another interesting hole. Great angled drive over the dune. If the rough was grown up a little on both sides of the fairway, can make the hole play tough. Another great amphitheater.
Hole 15. Par 4. 455 yards. 15 on OC. This is the biggest hiccup in the routing. Quite a bit of a walk between 14 green to 15 tee. One positive: no other hole crossings in this routing. Negative: Crossing the width of 4 fairways. This is the last twist though. Smooth sailing back into town.
Hole 16. Par 4. 423 yards. 16 on OC.
Hole 17. Par 4. 495 yards. 17 on OC.
Hole 18. Par 4. 357 yards. 18 on OC. Like I said at the beginning, grandstand runs down the whole left side now. Mass amounts of spectators can finally see the last hole at an Open at St. Andrews.
In total... 7247 yards, Par 70. Actually 60 yards shorter than the Open tees at the Old Course currently, but reduction in par makes it play tougher than the yardage says and some vastly more interesting holes than say 3, 9, and 10 on the OC.