My solution was effective, but brutal.
CAREFULLY put a shoe on. You might need to buy Ø4 (or more) sets to get it right.
Take a drill with the SMALLEST bit you can find. (Yes, this got very bad very fast.) find the smallest screw you can. Drill through the shoe, into the foot, and screw the shoe TO the foot. Now insert the weight into the shoe. You’re now stuck with feet wearing the shoes, but they won’t disintegrate over time (or at least not as likely).
I also spliced the tending line to the top of the helmet.