The Bimmer's battery compartment is looking a lot better after a good clean and a serious seeing-to with a wire brush. With the surface rust scraped away and the whole area wiped and dried a second time, I applied some rust-inhibiting primer and left that to dry overnight.
For now, I've lined the area with some thin cardboard and seated the battery on top of that, but in the coming weeks it'll get another coat of paint - probably black or dark green - and that should, hopefully, be the end of all that.
The new battery has been behaving itself, too. It's brilliant; luxuries such as being able to drive with the headlights switched on are now a given. I did return from two and a half weeks away at Christmas to no power, but I'd forgotten to disconnect it beforehand, so I can forgive it that.
On to more interesting things, then, such as sorting out the way it looks. First to come off were the Heko wind deflectors, which seem pointless in a country that enjoys only a few weeks of proper window-down weather each year. I approached them with caution, spent some time looking for fixings, then got bored and yanked them off. Turns out it was only adhesive, and the car looks immediately better for it.
Next, the wheels. My colleagues' initial horror at the 5's Alpina-style 18in jobs moved gradually towards mild distaste the more it hung around the car park. I thought I was sold too, until a set of original 15in cross-spoked BBS-style wheels with (just about) legal tyres popped up on eBay. The hammer fell at £100, and they're now waiting to go on.