Well, I used the basic instructions posted here and on TFL and managed to get it broken down (though I couldn't get the bolt out of the receiver), cleaned and back together. I notice today at the range that I think I put the magazine tube cap retaining pin (it has two screws to hold it in as well) backwards. It wasn't going anywhere and the magazine tube wasn't twisting out, so I shot it as is with the intention to switch it later.
Basically, got everything cleaned up, removed the magazine plug and it shoots great! What an incredible clay gun! It has a 30" barrel with full choke, so I can really get the long ones. Though I've only shot clays (or even shotguns!) a handfull of times and am still perfecting my techinique.
One problem that I had (even before tinkering with it) is the rounds don't like to stay in the magazine tube. They rest on the "gate" (sorry, I don't know shotgun terminology) and when I try to put another round it, I have to keep them all from popping out. Basically, if I pushed the gate up, they'd all come straight out. My friend's Rem. 870 has a little spring loaded tab to hold them in there, if that helps. My Model 12 doesn't have anything like that.
Anyone have any ideas?