The evidence is still fairly inconclusive on back/side sleeping. I'm a health scientist to I read the paper when I was pregnant with my daughter. The NZ study (which is the only study really about this) found an increased association between back sleeping and stillbirth in women in 3rd trimester (not 2nd). But correlation is not causation and there is no evidence that back sleeping causes stillbirth. It's entirely possible it's a third factor altogether that is associated with both back sleeping and still birth (sleep apnea for instance, which would be heightened by back sleeping and would reduce oxygen intake in mums).
They also found the same correlation with sleeping on the right side, but not the left. Interestingly, they found the same risk applied to not getting up to wee loads during the night. Women who wee only once or not at all during the night were 2.5 times more likely to have a stillbirth than those who wee twice or more. Taking a nap during the day (no matter how women slept) was related to 2 times greater risk of stillbirth than not napping. It's entirely possible that there is some lifestyle factor related to all of that - women who are not well, struggling with pre-eclampsia, GD, some other pregnancy complication who are off work in 3rd trimester, may be more likely to nap. They might have other issues that mean they aren't producing the right hormones they should that lead to extra trips to the toilet in the night and they sleep more deeply, with less tossing and turning, so more likely to sleep on their backs. Or they might be more overweight, have existing health problems that prevent them from sleeping on their sides (chronic pain, etc.). And it's these things that are actually what cause the increased rate of stillbirth.
Basically, my point is, it's just one study with a very small sample size and there is no evidence that sleeping position causes stillbirth, so take it with a grain of salt and don't stress too much about it. I found it uncomfortable after a point to sleep on my back and that's been I stopped with my daughter, but I wouldn't worry to much if you wake up on your back as you can only control so much.