I suppose you stay near Regentville at Hougang Ave 9
I tried both routes (the one you suggested and the Jalan
Kayu->TPE route)
The Jalan Kayu one is definitely more expensive as you enter TPE
much earlier than at Hougang Ave 3 where you can choose to enter
Old Tampines road too.
Its rare for Old Tampines road to have jams (personally I have
never encounter any before). But one point to note is the Kovan
area always jam in the morning so maybe the TD was imply that
area.
Another route you can consider is Hougang Ave 9->Sengkang New
Town->TPE. Smooth traffic flow and cost about the same as the
Old Tampines Road
that's the problem, I'm not well verse with the roads. I can
only rely on following bus routes.
all these while, I avoid staying up late so that I don't wake up
late. I don't trust cabbies anymore.