Thanks for listening!
I let this sleep for two days and read your comment, and this gave me a new perspective about things that could do better. I still don't know for sure what to do next, but the things you are having problems with happen to be the things I'm most unsure about, so at least I know where to look at. As usual, your help as "educated fresh listener" helps me focus.
I took action using your feedback as starting point for "where to look at":
I asked the singer for a new recording, pointing out that although not being exactly in key can give a certain style and attitude, in some places it went a bit too far. Once you pointed it out, it yells at me every time I listen to it.
I reduced volume and removed a bit of the FX in the "Korg layer" of the drums. I'm pretty sure the overprocessed Korg Gadget drums are what is popping too much.
I reduced the reverb and the stereo spread of the vocals. They don't lose presence, but they have less processing now. I may have been abusing reverb and stereo spread for the vocal track.
I uploaded a new version for now and I'll wait until the singer sends me the new recordings.