thx jbbebg. No worries, i'm far from an electronics expert, but i won't make a mistake with the polarities. Got the battery today. I wasn't planning on wiring the new battery parallel to the old one, so i took the old one out.
Too bad the new battery is a little too high to fit inside the case. Maybe i'll have to cut a little piece out of the backside of the case and then put some cover over it, like you suggested. For now i drilled a little hole in the back of the casing to fit the wires through and taped the battery to the backside. Before i do some more handywork, i want to test the new combination. Everything is working fine right now, but i want to be sure what happens to the battery indication after charging etc.
I'll be back when i know more. This might take some time though, because of the learning curve of the battery circuitry, like you mentioned.