PC (Facebook) Map
Here is a route through Birthday Island that gets all the dragon pieces for the PC version. Click on the image to get the full resolution. The Mobile version is mirrored vertically.
The total cost is 58330. This is a problem because the quest is only 20 days, and you can collect 800 points every 8 hours. So you have 800 * 60 = 48000 points you can collect naturally.
There are 7 known pieces for old dragons that could be cut out. 4 for Poseidon, 1 for each of Hades, Cerberus, and Blue Flame. So instead of taking the gray path, you’d use the RED shortcuts. That gets the total cost down to 51290. UPDATE: Taking the optimized PINK routes gets the cost down to 50640.
It should be possible to get the cost down the other 3000 points or so to get below 48000 by skipping other “?” pieces along the way when you can tell they would be a piece for a dragon you don’t want. They will be different dragons for each pplayer, so pay attention to the distances to the next piece, especially before heading down any of the “spurs”. Those are the dead ends you would backtrack. You should be able to tell if those dead end pieces are ones you want to skip or not.
The costs aren’t marked on the mobile map, but the costs will be the same as on PC (Facebook).
For those who would like their own blank maps to print and plot their own routes on, here they are: