To add my experience, I’m in the UK, and I’ve tried various kinds of AA battery - some the same, and also mixing brands, as suggested - and none of them fit. You can try and force them, but it results in the main casing bulging outwards (and would surely crack in time), and the back cover not fitting on. AAAs do make it work, but you have to pack the battery compartment with something to stop them slipping out of the terminals. I’ve managed to make the volume turn up and down, but it took a bit of fiddling about, and had I not read how to do it here, it would already be in a jiffy bag and going straight back to Boomkat.
Basically, it’s no good at all and a real disappointment, particularly as I’d bought one for a friend’s birthday (no need for my life story, I know, but that aspect has pissed me off a fair bit). Christiaan, as far as offering all this advice on which battery brands to try, I’d perhaps be more seriously considering recalling them if this is a widespread issue. And offering refunds. Countless other products manage to get batteries to fit. I’d argue it’s a bit more serious than issuing a list of the types of batteries which work. Unless my unit is an anomaly, of course. but it doesn’t sound like it.