Models breaking in LAN

I've been working on a mod in which one of the main features is a set of items (not armor, just normal items) that get automatically put in the head slot with the use of a GUI button. I used a custom blockbench model to make it render in 3d around the head. The issue is that, despite it looking normally on my own head, if I open another client and have both clients in a LAN server, the model will flicker on and off on the other player (the player coming from the client opposite the one the flickering is on). The flickering happens to all 5 of the custom models, and doesn't happen to the players from their own client. I haven't tested this in an actual multiplayer world, but since that's what the mod is being designed for, I'd rather not take the risk. How do I fix it?