The symptoms you describe are not entirely consistent with the conclusions being drawn.
It may well be that there is air in the system - the SMC will move only 2mm when it is new and bled properly. I know, I've just replaced mine and the pistons seals in all 3 calipers and thoroughly bled it. It is better than it was when new. Much more than 2mm and there is probably air in the system still.
But the SMC being unable to move after being ridden is an issue and that isn't caused by air in the system.
What position is it stuck in ? released, or applied. How do you know - it can be stuck in either position and both will feel the same - stuck ! Given that you have free movement when the 'brakes have cooled down' and that you can apply the rear brakes using the SMC and they release when you release the SMC, it suggests that the SMC movement is OK. (But it doesn't prove it to be OK).
But go and press hard on the rear brake pedal, and then try it again. Is the wheel free to move ? Do you get the same movement out of the SMC ? or More ? Or less ? Is the rear wheel then free after you release the SMC?
(If you can get a friend to observe the behavior of the SMC when you return from a ride, and get them to watch what happens when you press on the brake pedal, they may observe a movement of the SMC away from the fork leg. That would be an interesting and revealing observation.
Also, you may observe that with the rear brake applied, you cannot move the SMC. Get a friend or put a weight on the pedal to apply the rear brake, and try to move the SMC. The brake pedal will push the SMC way from the fork leg into its relaxed position. After pressing the SMC by hand, any movement at the SMC by pressing the brake pedal would suggest that the SMC is not returning fully to its relaxed state by itself. This may be due to a problem with the SMC piston not clearing the SMC compensation port, or it may be that the port is clear but fluid is able to escape for some other reason. The next items up the line (apart from the delay valve) is the rear brake master cylinder. It may be that the rear brake is applied, blocking its compensation port, or perhaps the returning fluid cannot escape into the reservoir - maybe because the reservoir is too full.
Check the level of fluid in the reservoir. It is not unknown for fluid to be topped up during the lifetime of the brake pads, and then when new pads are fitted, pushing in the pistons returns more fluid to the reservoir than the reservoir can accommodate.
I have a couple of articles on the forum. A few 'gotchas' which can affect the braking system irrespective of any bleeding issues, and some observations of how the air bubbles can hide when bleeding.
If you haven't read them, they are worth it. Not just my opinion - there are a couple of dealers around here that I know have used my notes !!
https://www.st-owners.com/forums/showthread.php?135125-ST1300-Brakes-Avoiding-the-Pitfalls
https://www.st-owners.com/forums/sh...0-Getting-all-the-air-out-of-the-brake-system
But if you can do those simple tests with your brake pedal and SMC and let us know what you find, it might help to identify why the SMC seems to be stuck and then becomes free.
Of course, it might be the start of the dreaded SMC problem where crud at the 'open' end of the cylinder is preventing the return of the piston and the expansion of the hot brake fluid in the rear line is causing the locking - releasing as the fluid cools. But you might expect in that case that when you apply the SMC by hand, then release it that this would also not allow the brake to release as you describe that it does.
Your bike is 16 years old. A faulty SMC might well be the issue. The design was changed in 2008 and the new design will not fit the older bikes without changing the calipers as well. The 10 year window for the supply of parts for 2002 to 2007 bikes has just passed. You might want to get an SMC anyway, while you are still able.