I wonder if the OP hasn't quite appreciated the distance from Singapore to the equator (it's not like it just skirts along the southern fringes of the island).

A quick google suggests it's 85 miles - that's a good few hours on a decent ferry. I could probably dig out my old edition of "S E Asia on a shoestring" but the map posted by jpatokal probably flags up the place I managed to get to on the East coast of Bintan. It rained for two days solid whilst I waited for the boat before giving it up as a bad idea and retracing my route which I think was a share taxi across Bintan, boat to Batam, bus across there then a ferry back to Singapore. I then managed to keep going and all in the same day made it to Mersing. Got to Tioman a day later and the sun was out. Paradise!