So… as I indicated before, support sent me a free new battery after I contacted them. In fact, I had already placed an order for a new battery and they saw that and paid the money back without me asking them to do so - great support there! Oh, and by the way, my old battery started bloating as well…
After using the new battery for 2 weeks now, it seems to be working fine. So, although some here might suggest that the problem is not the battery, it seems that - at least with me - it was exactly that…