I'm not currently using iTunes-Match on my phone, but I think my use of it in the past corrupted my music list on my phone and it had this same skipping problem. I couldn't listen to half my music because it simply skipped past it (2 or 10 at a time). I removed all the music syncing via iTune, so iTunes said there was no music. Yet there were still 20-30 songs on my phone.
Your steps for deleting all music data from the phone seems to be the thing I needed. After removing all music via iTunes I used your steps to delete all Music from my phone. Then, when I re-synced music from iTunes it all started working again
Even if you don't want to use iTunes-Match, if you have used it in the past, it has likely corrupted your music list on your phone. These steps to remove all music and re-sync from iTunes may solve your issue.
Note: I had already hard-reset my phone, and restored from a backup. But I restored a corrupted music list, so that didn't fix my issue. That's why this option worked better for me.