Bizarre charging behaviour

You don't need to do it all in one run, though that would be better for the charge chip to learn things properly. But in terms of getting it properly charged, you could charge it while you're free, taking it off charge again before you go to bed or go do something else. It's showing no indications that it's likely to explode at present, that's just a trick I learned for when you're charging something you don't entirely trust yet.
do it all in one run, though that would be better for the charge chip to learn things properly
I already spent a day doing that. see earlier posts.

taking it off charge again before you go to bed
Which effectively makes it a paperweight, because I'm not confident enough that I'll remember to take it off the charger every time I leave it unattended. Given the potential consequences, this means I'll tend to just leave it unplugged. And given that the wall charger has broken I won't be able to resurrect it if the battery discharges completely.
I already spent a day doing that. see earlier posts.
Yes, but log it so you can compare logs and see if the full value is changing at all. You'd need to do two charges to do that, because the logs only report that stat the once.

Edit: I haven't seen you saying the wall charger had busted before now, only you saying you were using it on the previous page and the log showing the unit seemed to be charging well until the point where you unplugged it. There's weird behaviour with the charging light in the OP, but going on the evidence of it charging perfectly well in that log I assumed that had resolved itself.
Okay, that all looks good. First time round it didn't quite make the value it recorded as being at full charge. On the second charge cycle it got over the recorded full value. I don't know where it gets the battery percentage from, so I don't know why it claimed it was at 100% when it was still a way off the stored full value, presumably it's using some other value that it's not exposing.

It would be interesting to see how far it would get if you didn't unplug it. It wasn't even starting to tail off the first time it thought it had hit 100% and stopped charging, when you did unplug it it was starting to fall from a maximum of 1734 down to 1150. But I don't blame you if you're feeling scared by it falsely claiming it's over 100% full. Hopefully it's learning, but those logs don't record what it think the battery percentage is. Comparing the log from today and the one you posted before the full charge level actually fell, proably because it never exceeded that value during that run. I assume that's written out at the start of logging, so I'd expect the value in the next log to be higher. Of course I don't know how that will help given it doesn't seem to be using that value for the percentage indicator, but at least it's learning that your battery isn't as knackered and old as it thought it was.
Hmmm. Interesting. It's still discharging at the moment. I might put it in a box or something and just let it charge over 100% while I'm sitting here. I'll let you know how that goes when I post the next log.
Hey, sorry about the slow reply. I didn't get to this the next day. I've now had it charging for the last ~36 hours and I'll have a bunch of logs for you soon. it's charging at the moment and over 100% but it only seems to be going up very slowly now.

I'm thinking that maybe because it's rarely discharged (it usually sits on the charger with a relatively full battery) that perhaps the pandora and/or battery has become confused about its charge levels. I'm thinking that a few full charge / discharge cycles might do it good and help it to recalibrate itself more.

I'll report back with a bunch of logs and screenshots in the next day or so :)