Thanks for your fast reply!
I think I might understand a little bit more what I need to do now.
I'll install Bitcoin ABC on an external HDD and let that sync until it's done. Then I'll set my Armory path to that external harddrive. Do I still need to delete some blocks then? According to the BCH network (or whatever it's called) I have not spent any BCH since the fork (even though I've spent BTC since the fork)?
You're welcome, and you're close. You should be able to copy your Core data and Armory data over to the external drive. (Make sure they're copies!) Cash should do a large reorg and reset the blockchain, downloading only the data starting from the split. The Armory wallets will work as-is but you'll want to use copies since the wallets themselves (and the Armory DB) will split once you use the coins.
I still can't see my current BTC balance,
Are you running Armory and Core at the same time? What exactly is happening?
would it be wise to first send my current BTC balance to another wallet so I don't fuck up, or is it literally completely impossible to fuck up?
Send the Bcash coins first. Cheaper fees, and they're the ones you want to move anyway.
I have one question about a line in the log file:
"-INFO - 09:44:27.000: (c:\users\goat\code\armory3\cppforswig\BDM_Server.h:263) Listening on port 9001"
I know goat is one of the developers of Armory, but is it trying to access his user or something? Because I of course don't have a user called goat on my computer.
No clue. Presumably a bug in the logging code somewhere. Don't worry, goatpig isn't after your coins.

I can take a peek around the coins and see if I can figure out what's going on.