Finally couldn't stand the lag and called Starhub's helpline. Very patient service as Technical Assistance talked me through the diagnostic procedure. Despite long pauses in between instructions as I connected and re-connected cables and waited for a test file to download, there was always a calm, reassuring voice at the other end of the line telling me the next step. And this was already close to midnight, mind you. Someone was available even past midnight to entertain my queries.
Didn't get immediate results, but the problem at some point seemed to correct itself. But they promised me they'll still keep looking into my original complaint so that it doesn't happen again.