What to Do?

I think I would probably ream out the chamber, and then do a salt/alcohol - cotton ball/alcohol treatment. Run some Everclear-soaked cleaners through the stems, then put the stems in a solution of Oxyclean and warm water for 15 to 30 minutes, take 'em out and rinse 'em off, then scrub 'em down with a Mr. Clean Magic Eraser. Then I would apply some olive oil. Just because I haven't gotten around to ordering any Obsidian, and my B&M and local smoke shops don't carry it. I would also most likely clean the shank out with some Everclear. I don't know what I'd do with mold on the rims... probably scrub 'em with spit and paper towels. What say the Sinister Six? LOL ::

There's tons of info all around this site, just gotta keep poking around because there's so much of it and it's best to bookmark something you find interesting so you can call upon it at a later date. The search function is a bit wonky but we still are able to find stuff!
The first link is to a very useful thread for you. The second link is to an article about generally how to go about a deep cleaning, and the third link is an easy step by step with pics on how to remove oxidation from stems.
http://pipesmagazine.com/forums/topic/oxidation-removal-on-stems#post-218625
http://pipesmagazine.com/blog/put-that-in-your-pipe/briar-pipe-repairs-home-remedies/
http://pipesmagazine.com/matchstickman/pipe-smoking/from-stem-to-stern-pipe-stem-restoration-with-no-buffing-wheel-or-power-tools/#comments
P.S. The salt alcohol and the cotton alcohol treatment are exactly the same. You're just replacing the salt with the alcohol as some do not like the extra clean up you have to do with the salt... and if you dare forget about it the salt will be rock hard and stuck inside your pipe. Cotton ball method is just easier.

I don't think you have to be TOO delicate with the salt/alchohol treatment. I'd start by folding a pipe cleaner in two and stuffing it in the shank, making sure it just barely pokes through the draft hole. Then fill the bowl with your salt (I think it's supposed to be non-iodized), and a few drops of the Everclear. I like to do this in 1/3's. Fill the bowl 1/3 of the way with salt, then Everclear, then another third salt- everclear, and then fill to just below the rim with the last bit of salt, and top with a few more drops of Everclear. Let that sit for two or three days, then- take your czech tool, or what have you, and use that to gently scrape out the dried up salt. Finally, wipe her out with a few pipe cleaners and allow to dry for another two or three days.
Yes, regular store bought Oxyclean is what I used. Powdered version my friend.
The salt, and the cotton balls, as I re-collect, are used to absorb the tars and oils that the Everclear draws out of the briar. So, either option works as well as the other, cotton balls being less messy.
Here's a thread that I found, that lead me to using the Oxyclean on some recently acquired estates.

http://pipesmagazine.com/matchstickman/pipe-smoking/from-stem-to-stern-pipe-stem-restoration-with-no-buffing-wheel-or-power-tools/
I didn't bother with the micromesh, so my stems are black, but not glossy.