We updated all mods we currently run, per Uveso's advice. After that didn't solve the desync issue, we finally checked the Mod Manager on my brother's PC, and found some quite old mods that had no business being listed. It turns out there were old copies of mods found in the folder "\steamapps\common\Supreme Commander Forged Alliance\mods". I don't even know how those got there. He deleted that folder and we got everything working fine in multiplayer, no desyncs at all with any combination of mods.
Thank you all for your patience. (This is embarrassing. I swore I wasn't gonna be the guy who asked for help without first checking all of the extremely obvious solutions. I feel very stupid now -__- )