I have an odd idea for this challenge. It involves a very specific proof game construction. So pay attention!
White and Black cannot move more than one pawn each throughout the entire game from the starting position. No captures are allowed whatsoever.
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!
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.