Maybe I'm doing it wrong, but so far I have only had success finding cards I need by using the trading opportunities link. Even then, it is a long process to find people who actually have the versions/conditions I need.

I am trying to eventually make a set of Alpha Commons/Uncommons, but it seems like there is not an easy way to find other traders who have Alpha cards in their tradelists. Again, it only wants to show me all versions of a card like Lance, for example. Is there a better way to quickly search for members who have the specific cards you're looking for?

Well all of the traders listed on the opportunities page have something with correct cards you need. If you click on their name, then on that page select "Strict Matching" on the widget that shows what they have - those are the cards that "matched".

If you want to search for people who have only one specific card, you can add that specific card in the "I'm looking for" field, and set the Alpha edition on it