I've finished part 1 of the system I want to place in my custom mode. Here is a bonus thing you can add in your game that will influence nothing, that can be fun to see.
Help by Achilles and inspiration from the Taunt Battle code from Dan Salvato.
Code below has been fixed so that a game is won by highest amount of stocks instead of most coins.
Coins in Stock Mode (1.02) [flieskiller]
04167f78 60000000
04167f84 60000000
0416B0CC 38600001
044ddc28 41300000
0416597c 480000CC
C2165A64 0000000C
3E208046 6231B6A0
8A310000 2C110000
40820014 3E208045
62313110 3A000E90
48000010 3E20804A
623113CC 3A000050
7F53D378 2C130000
41820010 3A73FFFF
7E318214 4BFFFFF0
80110000 3E208016
62315AA4 7E2903A6
4E800420 00000000
(edit: total screen height is different from Dolphin and console, and I didn't know that, so I increased the height a bit, from 41500000 to 41300000 for being able to see it on console with a TV)
(edit 2: Because of not enough testing, when a game was finished, the team with highest amount of coins was winning instead of the player with stocks left. I modified so that it was right for stock mode. Here is in the spoiler the old version with most coins winning the game:
result: The coins are dropped like in Coin Mode, but in any game modes. In addition, the Score Display number appears under the characters logos and shows the amount of coins the player has.
ASM notes:
Video showing this (with no sound and low quality):