There really is no need to back up your xprv. The xprv is derived from the seed phrase, so if you have the seed phrase, then you can easily obtain the xprv. Further, backing up an xprv is far more prone to error and if you do make an error, far more difficult to detect and correct compared to a seed phrase. If it were me, I would simply use both devices to back up the seed phrase so you have two back ups.

In terms of the derivation path, as long as you leave it as the default then I wouldn't worry too much about backing it up. Electrum will automatically detect the seed phrase type and restore to the correct path, and in the highly unlikely event that all copies of Electrum have been scrubbed from the internet in the future along with all information about what derivation paths it used, m/0'/0 isn't exactly super difficult to brute force.