If you want a janky setup for it I have one for you and its probably slightly better than the fish tank condensation collector. Turn your heating to full power, then connect the heat pump to a tube that takes the cool air and directs it to you.

Optional: Watercool your sofa by putting a few PC rads next to the heat pump and they pump water round a hose pipe on your sofa. Turn off the radiator in the room you want cooling in.

I have been kinda thinking of the hosepipe watercooled sofa idea myself though without using the heat pump for it, just a bucket of water and a pump, put some ice cubes into the bucket. Or freeze a 2L bottle and put that in. Avoid thermoelectric, its inefficient. Passive cooling or perhaps make use of cooler underground temperature are also interesting thoughts. But in reality I doubt I will end up doing something like it and it just remains in the idea phase.

You could probably gat away with it if you install a single mini split somewhere upstairs to remove moisture and cool the rest of the house with the big pump

You would probably end up with the same condensation issues there then. Unless the system is build differently to start with to consider that, but at that point you are replacing the entire system anyway.