If I had to guess my first thought would be to base it in pieces to place at each step, making the optimal splits:
5: 48/36/20 or 46.15/34.62/19.23%
6: 96/48/20 or 58.54/29.27/12.20%
7: 144/60/20 or 64.29/26.79/8.93%
You could also calculate it on optimal move count, but I have no idea where to start on that. Stickers to place would be another metric, that would take into account the extra difficulty of lookahead and maintaining the centers while edge pairing. That would result in splits of:
5: 48/72/48 or 28.57/42.86/28.57%
6: 96/96/48 or 40/40/20%
7: 144/120/48 or 46.15/38.46/15.38%
Not sure if that's the answer you were looking for, but at least it's an interesting answer to calculate.