Hi Ian,
I did this wonderful trip a few years ago. You are only in each hotel for a couple of nights. There may well be time to get laundry done, but I would suggest taking clothing (i.e. Rohan/Craghoppers etc.) which can be washed and dried overnight. You have a lot of very early starts. The only time I have ever used a hotel laundry service (in Thailand) they used biological soap powder and I itched all the way back on the plane to the UK! Travel wash is the way the go!
Enjoy!
Cheers,
Hils
I have been to many Asian countries and agree with everything Hils says.
I always try and take all quick drying travel clothes, I try and keep up with my washing so that I never have too much to dry and I try not to wash clothes on a one night stay. If you are desperate you can roll a wet item in a spare towel, walk on it to squeeze a lot of the water out and then hang it up.
In some countries if you send clothes to the laundry and they are sent out they may be washed in the river.