I would like to thank everyone again, especially for the many links and tools provided alongside with some good explanations as to why many accounting systems today still are so arcane and archaic. If you run a small or medium-sized business and experience similar accounting woes please have a look at the comments for highly useful accounting tool suggestions.
One particularly interesting solution that came up in those comments is LeapIN. Building upon Estonia’s e-Residency programme LeapIN provides a turnkey business operation including incorporation, a bank account, accounting, taxes and compliance. While it might not be for everyone – it doesn’t sound particularly useful to already established businesses – this certainly is an intriguing approach, especially for location-independent online businesses.
Anyway, here’s how I finally went about solving my particular automation problem: After quite some research I found Banking 4 by Subsembly. Banking 4 (available for OS X, Windows and various mobile platforms) is an online banking software that allows transaction data to be exported in the infamous MT940 format. This data in turn can be imported into my accounting software Collmex.
Not a completely automatic solution, mind you, but much better than manually entering accounting entries.