you control your private keys via seed, but getting the individual keys per address is gonna be a bitch. i have a ledger too and i put my btc on a paper wallet because of this.
you can download pages that'll decipher the private keys of your seed, but the first time i tried it i found the private key i wanted in a couple of minutes. next time i tried i gave up after checking 1200 addresses.
there'll probably be a btx wallet that uses a seed along soon enough. all you'll need to do then is move the btc out of the ledger, use the seed with btx and then get a new seed for the ledger.