I do understand that most people will not have the time or will not bother reading through all the advice given in the massive battery problem thread. So I just want to repeat my experience here and I hope it will help someone.
Ok, my 4S is now working completely as expected.
I'm not sure which step did it in the end, so I'll just repeat my experience.
I did the 'recovery mode' restore first (google for 'iphone boot recovery mode' to learn how to do this). After which I started from scratch (using a 4S backup should work as well) and disabled the often mentioned notifications (disable calendar) and location services (disable time zone) that seem to cause trouble.
After that I did a full discharge and charge of the phone.
That made a huge difference. The phone still discharged too quickly but it was A LOT better than before, especially when actually using it (as opposed to it being on standby during the night)
And this is where the magic probably happened.
I did a 'restore settings' (which doesn't wipe the phone: General > Reset > Reset All Settings), disabled the usual notifications and location services again (see above).
I then used 'Battery Doctor Pro' to do a charge with trickle charge.
Went to bed, phone 100%.
Woke up, phone 98%
4hrs later with moderate use (email, texting) but lot's of driving (so network searching)
I did my second trickle charge yesterday evening. Went to bed (battery 100%) woke up in the morning with the battery still showing 100%
8hrs later with fairly heavy use (emails, calls, text) and mast jumping (driving), notifications, Siri and location services switched ON.