I suggest you do some research on climate in the different areas. Wikipedia usually has good climate charts for towns. Other sites like wunderground.com have good historical data.
Having said that:
NZ will be cold and wet! The far north will be better but I wouldn't cycle July to Sept. Also short days for cycling.
In SE Asia it is the SW Monsoon season, so expect hot and wet. Probably not as hot as when I was last there in April at 42 degrees, as high humidity keeps temp down. It is still cyclable and plenty do, but you have to keep an eye on flooding, washed away roads, etc.
Probably the best areas will be the East coasts of Malaysia and Vietnam as they are more sheltered from the wet SWerlies.
Beware Chennai after Sept as their Monsoon, the NE starts about then. Great time for west coast in India.
I think the bottom line is that you are in the wrong place at this time of year. You could try Indonesia which should have better weather this time of year, although still hot. Look at AirAsia for good flights with reasonable charges for bikes.