First, out of curiousity has anyone been able to find a manned booth to politely ask for an exit passport stamp, at Changi Airport or Woodlands CIQ? I collect these and wouldn't mind the extra effort if it's even possible.

Second, what would be the ideal way to get from Changi Airport to JB CIQ, be in JB for a few hours then get down to the Gardens by the Bay? This would be on a Thursday.

From what I gather: Changi MRT -> Woodlands Train Station -> buy KTM train to JB CIQ. Then on the way back, take the KTM train back to Woodlands CIQ and MRT down to Gardens by the Bay?