Well, I completely nuked WinAmp and have gone back to basics. Otachan's ASIO seems like a rather outdated app/dll.
Therefore, I used WinAmp's ASIO holder and ASIO4ALL. There was another option for ASIO labelled "cmasiopPCIX" but using this caused clicking effects
Anyway, I got ASIO4ALL setup and working as can be seen in the screenshot below. Note Windows Sound showing silent despite the music playing which proves that music is bypassing the Windows stack!
No skipping at all so far
I'm so happy!
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I used a thumbnail because original image is large. Click to open:
