Create a 94 move long game in forward going chess

Forward going chess has the exact same rules as classical chess except that the rank of the square to which a piece moves always has to be higher than the rank of the square from which the piece was moved ( from the perspective of the side making the move ) - in other words with every move the pieces have to go forward. It is a consequence of this rule that castling is illegal.

Puzzle: Create a 94 move ( 188 halfmoves ) long legal game of forward going chess.

For the Nobel prize:

either

1) create a legal forward going game that is longer than 94 moves

or

2) prove that no forward going game can be longer than 94 moves

( Yes, I have a proof game of 94 moves. )

Your knights jump two ranks at a time, you are wasting moves this way.

Maximum without collisions: 104 moves (pawns 8*6 + pieces 8*7)

Now we lose moves because of collisions - not all the units get to make maximum moves. Captures are also necessary, meaning some units don't get to make all their moves - i.e. we lose halfmoves. It remains to show each side loses halfmoves in a way that results in the fewest total moves lost.

The 4 rooks colliding with each other must lose 2 halfmoves, e.g. wRa1-a2-...-a7, bRa8xa7-...-a1, same for h-file.

The pawns, in order to get past each other, must make captures. Unfortunately there are lots of ways to do this. Each capture at minimum loses 2 halfmoves (since any piece captured on its 6th rank loses the 2 remaining moves.) The apparently optimal way to do this is for instance wPa2-...-a6, bPb7xa6 and all of the a- and b-pawns are clear; repeat for each pair of files, resulting in 8 lost halfmoves from 4 pawn captures.

Note that this capture scheme also means that the edge rooks need to capture 2 edge pawns still, in order to reach the 8th rank. So this is another 2 lost halfmoves that the pawns could have made.

Our theoretical maximum also relies on all units reaching their last ranks. Obviously impossible since there are 16 units per side and only 8 squares on the last rank. 32 units - 4 captured pawns - 2 captured rooks - 2 captured edge pawns = 24 units and 16 squares to fill. Therefore at least 8 more halfmoves must be wasted.

Our total wastage is therefore 2+8+2+8 = 20 halfmoves, which is at best 10 full moves. So 104 - 10 = 94 moves is the theoretical upper bound.

To complete the proof that 94 is necessary and sufficient, a sample game.

The proof is nice. I was almost there ( I had the 4 pawn captures losing 2 halfmoves each and the rooks never being able to leave their files most lose a halfmove on both the a and h file, but this simple math of how many pieces can reach the last rank did not occur to me - this was the missing link. )

The proof game I prepared as a solution kind of starts with sorting out the rooks first and results in a quite simmetrical and aesthetic final position:

I'm hasten to add that this is not my solution. Of course I could not solve my own problem. My only merit if any is that I could pose it.

What about something with a bishop or knight (or some piece other than a rook) capturing one or two of the rooks?  Would that make any difference?  (Just an idea I'm wondering but I don't really have the time to check/play out possibilities.)

I checkmated in 94 moves! Here's how:

https://www.chess.com/analysis/game/live/4769149113

Can you do it another way?