Derek C. said:
end up sat on the plastic base, which is the one thing I've been told never to do
Derek, the short answer is yes, this is a known effect and the cushion manufacturers describe it in their own instructions, so your clinic was right to mention it and worth going back to. As the cabin climbs to its cruising pressure, which on most aircraft is the equivalent of roughly 1,800 to 2,400 metres of altitude, the air sealed inside the cushion expands. The cushion firms up and lifts you out of it, and the immersion that spreads your weight across the cells is what you lose. On descent the reverse happens and it softens again. That matches exactly what you felt an hour in, and 12 hours of it is not something I would want you to sit through.
What people do about it is release a small amount of air once the aircraft is at cruise and the seatbelt sign is off, check the setting the way they were taught, and add the air back before descent, which is why it is worth setting an alarm for about 40 minutes before landing. The setting itself is the part I cannot give you from here, because it depends on your cushion model, your weight distribution and your skin history. The general check most people are taught is a hand slid under the seat bones with about a finger's depth of clearance to the base, but your own seating clinic set your cushion for you and they should confirm the check and the target for your flight, not a forum. Bottoming out on the base is worse than sitting on it slightly too firm, so if you are ever unsure in the air, leave it firmer and do your pressure lifts more often.
Two practical points on top of Sue's, which are good. First, the cushion goes into the cabin with you and never into the hold; if it is delayed or damaged you have nothing to sit on at the far end. Second, the altitude effect is one reason the whole flight needs a plan rather than just the transfer, and Marnie has set out what that plan looks like in long-haul flights in a wheelchair, including the pressure lift timing, fluids and the toilet question. What to carry on and how to protect the chair is in flying with a wheelchair.
Where I stop: how often to do your pressure lifts, what compression or clot prevention is right for a 12 hour sector, and whether your skin is currently in a state to sit that long at all are questions for your own therapist and doctor, and a 12 hour flight is a good reason to book that conversation now rather than in October.