I'm wondering how I might go about changing the models of all players on the team of the player who casts the spell, changing their damage modifiers, changing their weapon and mounting the new weapon, and restoring their health.

Any advice on the implementation of this? It definitely has to be client/server.

Long and short of it in one word: triggers.

The weapon cog/s to be used would need to be changed (weapon mounting/unmounting, damage modifiers), also kyle.cog (restoring health), the spell cog would probably just handle the keypress, keep track of any time limitation, and send triggers.
...I think.