Well, this is not based on my analysis of battery logs, but I think now I know how to make things work, and I have the log of what I did, so one thing can be checked against the other. Plus, I'll do it again soon just to check if I'm right and I'll log it again, so both experiences can be analysed under the light of the logs by those so inclined (sorry, but if something works for me in an apparently logical way, that's enough for me).
So... my original DR1000 battery was down to ~4hours of use, I replaced it with a higher capacity one and after one promising cycle of 18hours of 'work' with incorrect battery readings (in the end it wouldn't power on because the battery was completely discharged but the gauge kept reporting 100% till the very end) I was back to ~4hours cycles after that. That larger battery might have been damaged, so I put another DR1000 original type one and I was stuck with cycles of very similar length again.
Now I deem extremely improbable that any two random batteries can have so similar charge/discharge cycles so I concluded I wasn't doing it right.
What did I do in the end? First I set the DR1000 to never power off. I let the battery discharge completely every time, until the red light turned off (but not longer, to prevent overdischarging from damaging the battery), and charged it for a little while after reaching 100%. Now I'm back to ~12-hour cycles.
I assume the gauge gets used to the battery lifespan shrink over time, and when you put in a larger capacity / newer one it needs to go beyond its now-usual discharge curve to learn that the new battery still draws power...
Now that I got this working I'll try the same with that larger capacity battery I have, to check this is actually how the gauge works (and if the battery is actually damaged or not) and establish once and for all that it is feasible to use such batteries with the DR1000. I'll post the log for that here, but the post will go in this other thread about DR1000 and batteries