I think the reason why it slowdown even on 5 inputs may be because of the connection problem you might be using a broken USB cable
My assumption was this problem occurs while creating the transaction, but if you're right, it's while signing it. Is that correct, OP?
try to replace it with a known working one or try to clean the USB plug and terminals with a brush and thinner/alcohol.
I would not use paint thinner, that dissolves all kinds of plastic.
When I bought the Ledger back then, I thought I had made a good choice.
But now I don't have a good feeling about it anymore.
Unfortunately, what is on the ledger is not exactly small.
Still, 400 inputs isn't that much, and if that would be a problem, I would have expected much more complaints about it.
Should I rather get another hardware wallet and try to get my inventory over there?
That should work, as far as I know Trezor uses the same seed format. Whatever you do, don't enter your seed words in any website! You probably know this, but people still do it once in a while.
Alternative: use IanColeman's software to recover private keys, but this requires an offline setup and you should know what you're doing including offline signing. Another hardware wallet is easier and probably the safest choice.
yes, it occurs when signing.