Thanks for all your replies! It seems smorizio is closest to the solution that I found a few hours ago.
I was using the tool EasyBCD, that offers an option to rewrite the Win7 bootloader to the MBR. To my surprise, I was now able to boot Windows 7. Like smorizio, I believed that this was because of the old Win8 install that'd left some nasty bits behind.
Here's the strange thing: After I got it to work, I decided to boot Parted Magic and secure erase the whole SSD. I was expecting I could now directly boot Win7 after a clean install, without any fix. Strangely, it still didn't boot. So although the problem is solved, it feels a bit unsatisfying to know that I need to apply a fix everytime...
I did find out later on that this specific operation fixes the problem:http://www.sevenforums.com/tutorials/20864-mbr-restore-windows-7-master-boot-record.html
If anyone is willing to comment on this, please do so!