Just for the record, in case it helps anybody, I did update my Legder Nano S yesterday, I also had the Bitcoin app on it (I didn't know I have to remove it), the update went smoothly, I (re)installed the Bitcoin app afterwards and everything was OK.
I did use the original cable.
Why did you have to re-install, did your Bitcoin app got deleted? Afaik Ledger told us to delete all apps before updating in order to make sure that we have enough storage for the update. I'm not sure what will happen if the storage is insufficient in the middle of our update, but I'm pretty sure it can cause trouble if they don't implement a safety feature in case that happens.