Just so I understand this right... Would this procedure sound ok:
1) send my BTC from my core wallet v0.14.2 to Bittrex
Don't send to an exchange. Create a new wallet and transfer to it.
3) download, install and sync BCH wallet (which one is most likely not to cause any issues btw?) onto a separate PC
Electron Cash or Bitcoin ABC.
4) import private keys into new BCH wallet... will my BCH appear automagically upon restart/sync?
They should.
5) download, install and sync new BTC core wallet onto main PC and transfer the BTC previously sent to Bittrex
See my suggested change at step one. There is no reason to send BTC to Bittrex.