I have the original Bitcoin Core.
I thought that BCH has a separate address thats related to its forked BTC address, is that not true?
No. Bitcoin and Bitcoin Cash addresses/private-keys/seeds are the same.
Just empty your Bitcoin wallet by sending your coins to a new wallet (optional if you want to be safer), import your old seed in Electron Cash and spend your BCH.
Since the fork I've only sent a small amount of BTC once - that's not going to mess with my attempts to claim the BCH, right?
No.
If you had 1 BTC before the fork, you also received 1 BCH in the same address. So you should have 1 BTC and 1 BCH in the same wallet.
Now let's imagine that later you receive 0.5 BTC. Now you have 1.5 BTC and 1 BCH in the same wallet.
Thanks, that's very clear and straightforward.
Do you think I should I be running Electrum and Electron Cash on the same machine that I'm using for every day life? Or should I immediately get the keys and addresses for my new BTC and then delete Electrum?