Strange about the WH1000XM3s I haven't had that problem with the same headphones and an iPhone X. I have however gotten the same heat issues from time to time.
You can have it behave like a keyboard and simply 'type' the characters of the one time password in. I don't know how locked down your systems but usually keyboards are allowed.
Does wormhole do any hole punching yet? Looks like https://github.com/magic-wormhole/magic-wormhole/issues/6 is still open. I think if that issues gets tackled this would be a pretty amazing tool.