I've ordered a new
usb-serial converter. I didn't find one with 1.8v within Europe but I hope I can get it to work with a few modifications.
In the meantime the Kindle stopped charging from the wall charger (unfortunately I chose the cheapest charger I could find, it looks like it's dead) and after a day of not charging it was back to that big battery symbol.
So I thought I would connect it again to a PC and apparently the Kindle is still recognizable as a drive. Look at the attached screenshot from USBDeview. Although it doesn't show up in Disk Management, in Explorer it shows up as drive F: but it cannot be opened and there's no disk size next to it and it's greyed out.
As to why the battery is already empty again when the wall charger stopped working for a day or so, I can only speculate. Either
1) the Kindle was in the process of repairing something as I hoped and that process drained the battery, or
2) the Kindle wasn't doing anything in that time and the battery is just garbage