Never heard of the deep reset. I have noticed the "reset not resetting everything" issue in the past. Had to do a lot of resets after 3.0.2 and I got so sick of it I finally sucked it up and downloaded and started using the delayed reboot so I wouldn't have to do so many. Before I did though I would notice the same thing. One reset and I would lose my phone and wallpapers but AM/FM/Sirius presets were still there. Another one and I would lose presets but phone would still be there, and every other combination. Another one I noticed is that after some resets I would plug my iPod back in and it would resume playing from where it was before I disconnected it which means the reset didn't wipe out the index. The master reset is Sync support's first solution to fix any bugs you contact them about (followed by "take it to the dealer" second) and even their recommended master "bug-fixer" seems to have bugs.
Hopefully the APIM will work. I had mine replaced last June as the dealer was trying to fix my useless voice commands that were broken by 3.0.2. Unfortunately it did nothing to solve my problem. They remained unusable after the new APIM. Wishing you better luck! Hopefully it fixes your particlular issue.
.......here's a lockpick. It might come in handy if you, the master of unlocking, take it with you.