And after a lot of pushing around, I've finally got my miles credited on TK.

UA MP Compliance actually replied within a week and said that the miles were removed.
I filed another claim with TK but TK still says that SQ refuses to allow them to credit the miles.

I followed up with UA MP Compliance again and they confirmed again that it was indeed removed, but SQ's fantastic customer service still refuses to reply to any of my emails or give me a call on my phone.

I took things a little further and followed the procedures to file a data leak complain against Singapore Airlines.

The procedures required me to file a letter detailing what data I believed was misused and the incident and give SQ exactly 14 days to provide an adequate reply (similar to GDPR).
During the 14 day wait time, SQ refused to reply to any emails or calls (as expected of their customer service). On the 14th day, they gave me a "filler" reply tell me that they have received the email and are investigating it.

On the 15th day, I followed up with the respective regulatory department on this and they acknowledged my concern that my details were used to create a fraudulent MP account.

Magically, on the 17th day, the miles were credited but I've not heard from SQ nor TK about this as of yet.