OK, this was a frustrating experience but I'm (almost) there now. I used WinUAE to set up a CF-card, and got a Kickstart 37.300 ROM to replace the 299-ROM.
1. It was a bit difficult to get hold of WB 2.x. I finally found a set but the install-disk was corrupted. Piratebay then helped me to find images of 2.1, but also with a corrupt install-disk... Due to this I was unable to install Workbench the proper way.
2. I downloaded some freeware (?) HD-formatter from aminet, this tool (which I can't remember the name of) formatted the card in no time and started to install Workbench from the corrupted install-disk...
3. I manually copied the Workbench-floppy to the now-booting CF-card. I must say that Workbench 2 is not a very good desktop...
4. Downloaded tracktool and some games and copied to the CF-card.
5. Connected the CF-card to the Amiga for the first time. It booted and I could write ADF-files to floppy with no further problems

My biggest problem right now is that the mouse sucks. I have to build myself an optical Amiga mouse, and also a SCART cable for my TV. The 600's composite signal is pretty bad.
Next step: Upgrade to 2Mb chip-RAM and test WHDload.