I have had uncomfortable morning wood as well, though it’s only been occasional. But I know what you mean where it’s rock hard to the point of discomfort. It annoys me because it will happen early in the morning on a day when I would normally be sleeping in, and it keeps me from getting back to sleep.
If I get up to piss, that usually helps. I tried to jerk it away once, but my tolerance to stimulation in the morning is fairly high, and I couldn’t get myself off.