One thing I might try is getting rid of some storage
Careful with that. If the storage goes before the contents does, large piles can form. If the piles slip, spread, fall they can attract more stuff to live on top of them. It can cycle up to the next stage of hoarding by accidentally creating a "temporary" mess that then normalised.
Sometimes it's easier to know where to start and stake a claim to right of chucking. Like the fridge. Yes there might be chuntering about mould being cutoffable and eat by dates being "flexible", but rare is there much of a fight over a very liquid lettuce. Once emptied of crud, made sparkling clean and maintained as a non crowded, hygenic little oasis of calm in the storm it can be a talisman. It creates stark comparison to the chaos, beinging down the "normalisation of the hoard" a notch or ten. When feeling defeated, go stick head in fridge and feel less defenceless.
It doesn't have to be the fridge if the fridge isn't an issue. Maybe a small bathroom, or the kitchen counters, or the sink and draining board, child's bedroom. But it helps if it is a sliver of space where the hygene argument is undeniable to bolster fortitude in the face of high octane resistance.
Maintaining is essential. Before any new slivers are fought for and won, the already won places have to evolve into something that gets the attention it needs as a priority on a several times a week basis. Becuase they are the beacons that say it can be done, things can change and brace the backbone for more empire building.
Boy can you tell I come from a military background 
That bit is optional, see it as building a "garden of blossoming lifestyle" where precleared ground is nurtured into bloom and the weeds kept on top of,..or anything else that appeals personally.
I think as a place to start the above has an advantage over more drastic measures. The Hoard didn't appear overnight, and all that it represents won't be vanquished at the speed of light, but becuase it is a long, hard, slow slog, those little bugeoning Oasises can really help with the helplessness, powerlessness and ...knackeredness. It doesn't really matter if you are the kid, the spouse or the person struggling with hoarding.
Making little shiney spots of hope for something better in the home and making their maintence the priority goes qute a long way as a boost to morale and feeds the spark of working towards something better for everybody.