How do I pull it off without removing the funds from my ledger wallet and making them vulnerable? I create a new address, send my coins to it, then try to send a confirmation amount to the transition bot. Even with "Change address" setting unchecked on Electrum, by the time I'm sending the tip It's from a brand new address that has no association with the first and shows a 0 balance.

You have to do it the other way around:
send the confirmation amount first and after confirmation, send all your balance to this address!