You don't need FastDL or manual distribution (though that would work as a last resort). Just:
Rename the HUD image asset to something totally new and unique — avoid any name/prefix that exists in vanilla T6 (zm_rank, hud_, etc.), the same way you already did with specialty_.
Update every reference to that name: the material using it, and any GSC line that calls it (e.g. hudelem setshader "zm_rank1" or however you're referencing it) to point to the new name.
Recompile with OAT, making sure the new image name — not the original — is what ends up in mod.zone.
Test again over LAN or on the VPS.
With a non-colliding name, it should behave exactly like your perk icon: shipped along with the rest of the mod's new assets to any connecting player, with no need for them to already have the file locally.
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