In a comment on the answer to the PSE version of this question, linked in the other answer, user @Dennis Jaheruddin came up with a provable lower bound for this challenge.
"It takes 80 moves to move pawns forward. Obviously, they cannot capture the king and queen so there are only 6 promotion fields left on each side. Basically, this means it takes at least 4 halfmoveshalf moves to clear additional promotion fields. Then there are 8 pawn rows that block eachothereach other, each conflict will need to be solved by capturing at least 1 piece that is not on it'sin its starting position, hence we need another 8 half moves. Now we already have a lower bound of 92 and there are still some issues to solve. As such 96 is probably optimal."
Figuring out and provingroving that more four halfmoveshalf moves are necessary would be a momumentable achievement, finally bringing the 18 queens challenge to its knees. However, it seems no one knows where to start. Neither do I. As such, we are stuck at 92/96 proven plies. Hopefully, one day, a genius shall shine their light in our favor.