Yep that is the issue. GoD versions pretty much always share the same region restrictions as the retail release.
Unless something has changed recently, you can only switch your
account region every three months so if you did switch back, you'd be stuck in en-SG for that period on the 360. I've no idea how that would affect the Xbox One GwG offerings but the
Singaporean page lists the same games being available at the moment.
If you didn't want to dick about you could try and find a one month gold code and buy it with a new SG account then just play on you main account.