Recovering and casting indium
Through experimentation, I've come up with satisfactory answers to my problems.

1) What is the best material to cast indium in? Silicone rubber (the kind used for cookware).

2) How can I recovery indium that has "wetted" a stainless steel pot? Put the pot on the stove and heat until the indium is molten. Use a silicone rubber spatula to scrape the indium off, let it harden on the spatula, then pick it off. You can also use a wet sponge as long as it's the kind used for cleaning solder irons (make sure it's a new clean sponge!). I folded it in half and held it with a large clamp. That gave me something to hold onto.

3) How can I recover indium that has "wetted" glass, broken glass, or is contaminated with other odd bits of material? 

Number 3 is more involved, and I will break it down into steps:

1) Go through the material with a pair of forceps and discard any bits of glass that have no indium on them.

2) Place the material in Pyrex beaker.

3) Fill the beaker with mineral oil until the material is fully submerged (water may also work, but the oil will probably help keep the indium from re-wetting the glass bits).

4) Place the beaker on a hot plate and slowly heat up to about 160 degrees C (320 F). Periodically stir while heating (a screwdriver worked fine for me; I didn't use a magnetic stir rod because the broken glass might chew it up). Also, make sure your area is well ventilated; the oil will produce vapor.

5) Once you have reached 160 C, poke the indium and make sure it is molten. Increase temperature if it is not molten. Stir for about 30 seconds to break up the indium. Keep on heat; try to maintain ideal temperature.

6) Use a glass dropper to drop in 31.45% Hydrochloric acid (I used 4 drops total when the oil and material together was about 100mL). Add one drop at a time, and let the drops run down the inside of the beaker into the oil. (WARNING: This can result in splashing! Don't over heat the oil, add the acid drop-wise, and use proper safety gear: gloves, long sleeves/pants, face shield, and respirator with acid vapor cartridges). Adding the acid will react with the indium oxide layers and help break the indium free from other materials.

7) Stir vigorously with your implement of choice. The oil will become a nearly opaque brown with all the oxides. The stirring should also free up most of the indium from the glass bits.

8) When the oil seems saturated, thoroughly decant the oil into a waste receptacle (I used a mason jar). Save as much solid material as you can.

9) Fill the beaker with clean oil; do NOT begin stirring yet. Keep on heat.

10) Use your forceps to pick out the larger pieces of glass that seem mostly clean. Use another implement to scrape off little bits of indium from the glass bits as you are pulling them out of the oil.

11) Once most of the glass is removed, use strong stirring once again until the oil is mostly brown.

12) Using your stirring implement, try to push a good amount of the molten indium together into one blob on one side of the beaker. Now decant the oil into a waste receptacle.

13) Place beaker back on heat for a short time just to ensure the indium is molten. Make sure most of the material is in one corner of the beaker.

14) Use a broad-shaped implement (I used the flat head of a long "elevator bolt") to hold back most of the scrap material and pour off the indium from the beaker into a silicone rubber mold. The poured off indium should be MOSTLY clean. Repeat this step until you feel you cannot get anymore. Put the scrap material off to the side.

15) Once the clean blobs have hardened, dab them with a paper towel and cut them into tiny chunks with a pair of wire snips. 

16) Take each individual chunk and crush it paper-thin using a flat metal implement and a flat metal surface (I used an elevator bolt and a piece of sheet metal). This step is to find any tiny bits of glass. Glass has quite a different "crunch" than the typical "crackling" of the indium's crystal structure. You will know when you find one. Fine tweezers and some sort of magnifying glass helps.

17) You can now re-melt the clean indium into one chunk. I use a stainless steel shot glass and pour it off into a silicone rubber mold. If it's still oily, wash it with Ronsonol/Zippo lighter fluid, then rinse it with water. I actually chose to keep this piece of indium separate from my other indium pieces that I KNOW are clean. You never know, there might be one last sand-grain sized piece of glass in there.

18) As for the scrap material, there's still a bit of dirty indium in it. You can decide how hard you want to work and continue salvaging it. Use tweezers to pick out as much "clean" glass as possible. Wash it with lighter fluid and rinse it with water. Perhaps re-melt it in a steel shot glass and try to pour a little bit more out of it. Try putting a blob of solder flux in with the molten material and get it to stick to a copper wire. It's all going to be loss anyway, so you may as well try different things.

DISCLAIMER: I am not a professional! This procedure is not advisory. It is an account of my experiment and what worked for me.

If anyone has suggestions or constructive criticism, please feel free to comment. I know there are probably better ways to do this.