I have an odd idea for this challenge. It involves a very specific proof game construction. So pay attention!
Given that:
White and Black cannot move more than one pawn each throughout the entire game from the starting position. No captures are allowed whatsoever.
Construct:
A position whose proof game takes the longest shortest path to reach under the requirements.
Here is an example position.
- a4 h5 2. Ra3 Rh6 3. Rg3 Rb6 4. Rg6 Rb3 5. Rh6 Ra3 6. Rh8 Ra1
During the proof game, only a pawn per side moves and no captures occur. 6 moves is provably the optimal move amount to reach the final position.
Please leave a comment for any needed clarifications. Have a load of thought solving this!
Possible Hint:
RNBQKbNr/p1pppppp/8/1p6/6P1/8/PPPPPP1P/RnBkqbnr is one of my ideas. Finding the shortest proof game for it or a similar position may yield an a superb result.