It could well be the SMC which is not releasing the rear brake as it should (If the SMC fails to return to its proper position, the pressure in the rear calliper outer pistons cannot escape through the compensation port in the SMC). It is certainly a candidate.
But it could be something to do with the rear calliper itself. The pad pins could be corroded, preventing the pads from moving apart after the brakes have been applied and then released. The pistons may be having difficulty returning. The brake pads themselves may not be seated properly at the opposite end to the pad pins, or the silver retaining clip is clogged up with muck. The rear pads have a little notch at that end, and they match a small ridge in the retaining plate. Check that the correct pads are in there.
The pad spring can be inserted the wrong way round - there is a narrow strip and a wider strip on the 'H' shaped pad spring. The wider strip of the spring is for the pad that is next to the pistons. This is the pad that moves across as the pads wear down. The narrow spring has two tiny tags which are there to prevent the inside pad from moving towards the pistons - the inside pad stays put, and it is the calliper that moves across. If the pad spring is the wrong way round; if the little tags have been bent over; if the pads are on the wrong side of those little tags; if the two calliper slider pins are not clean and lightly greased; if the slider pins have too much silicon grease - then any of those things can prevent the calliper from moving back after the brakes have been released - resulting in brake drag.
If it is the pad spring that is the wrong way round so that the narrow strip is pressing onto the pad nearest the pistons, there is a period of time when it won't make much difference. Then as the pads wear down, the pad which is nearest the pistons will move further than the edge of the narrow side of the pad spring. The spring will spring down behind the pad and it prevent it from being released. The pad fits perfectly the wrong way round - it is a very easy mistake to make. On the ST1300A9, the modified front callipers have a redesigned calliper and the pad spring cannot be turned round. But the rear brake is as it always was.
While you are checking things over, just take a look at the rear calliper bracket stopper bolt - to make sure that it is located through the hole in the calliper bracket.
If you would like to see diagrams of all of this - then check out
Brakes - Avoiding the Pitfalls.
My guess is that if you take the pads out, release the calliper bracket from the axle, clean everything up, check that the pistons can be pushed in a little under thumb pressure (the outer ones can be see-sawed, the centre one requires more effort, but it should still move*) and reassemble it properly, then the problem will go away.
Unless it is the SMC that is the issue - but doing the above is probably an essential first step - and cheaper.
* nb Some sensibly say that you should open the bleed valve to test this, otherwise you may be pushing dirty fluid into the brake lines. I never let my fluid get that old.
I'm going to describe it as best I can. 
on the SMC failing.
