As far as i understood you, your BTC are not yet on your ledger. correct
Therefore you can not split them using any software from ledger.

Just do:

• Fully set up your Nano - done
• Get a BTC address from your Nano - ok, should be easy enough
• Send your BTC from your desktop wallet to your hardware wallet - the most intense step, waiting for the transaction to successfully clear  (not yet done, but will do it imminently)
• Get a BCH address from your Nano - ok (a receiving one, I assume you mean?)
• Install a BCH wallet and import your mnemonic code from your software wallet (not from your nano) - this is where I need the most clarification. First, do you mean install a BCH wallet on my PC? Like Electron Cash? Second, what is mnemonic code? Third, you mean import it from Electrum (which should now have a balance of zero, having previously sent my BTC to my Nano)?
• Send all BCH to your Nano - ok, should be easy enough
• Repeat the last 3 steps for any other shitcoin fork - ok