So, you went through all the climates and the map looks a mess (or not). Well, climates can be a mess, and the magic wand may not select some pixels, and you may have overlooked some combinations - the remaining is to be done by hand.

And we can start by the following
- there is probably an area very close to the equator that appears to be desert, between areas of savanna or monsoon... Well, it is savanna or monsoon! it's the rainy season in that region that doesn't match january or july (the ITCZ passes through in a different month, in its north-sound annual movement), so it slipped right under out radar.
- in some parts, a transition climate may not be appearing (like tropical monsoon between rainforest and savanna, hot steppe between hot desert and mediterranean, cold steppe between cold desert and continental, etc), add a strip of such climate manually and delete what was there before.

Then, you need to find out bits that aren't colored in any particular color and find the best fit manually (comparing with available information on Koppen classification, like I said before).

Thirdly, time to merge it all together and make it final. But I recommend you duplicate all the layers and simply merge the copies, just to be safe. Once this is done, you can smooth boundaries between regions, make very small micro-climate regions disappear if they are cluttering the map too much, etc.

After some work, including adding a key and a title (work-in-progress, still), this is my end result for the continent of Palamb:
FINAL (presentable).jpg