I also had a problem with teleporting because whenever I teleported my character using CFrame or Position, the attachments on my weapons and accessories would scatter all around the map making the hitboxes and shooting points really weird. I happen to have Commander 4 by Evo, so I looked into their teleport script and I noticed that they used SetPrimaryPartCFrame() for their model. I looked deeper and turns out there was a new version of that, PivotTo().
I switched all of my teleporting things to PivotTo(targetCFrame) and so far I haven’t run into any more attachment part problems regarding teleportation. I know this was a really late post, but I hope this helps!