I haven't tried the filament cutter mods so I cant answer that but haven't had a problem with my cardboard spools (Overture, Polymaker) outside of needing the rings to keep the cardboard from shredding.
A weight or desiccant pod insert couldn't hurt, but I only ever run into this issue with my 250g spools with printed adapters since they're so light with a long 'lever arm' from the center of the spool to the edge.
Also the only way to read remaining filament is if you add a Bambu RFID tag to the spool as this is what it uses to measure (counting how quickly the tag is spinning versus how much filament it has pulled).