Mods seem to be a better route to take when showing off design skills. SC2 is great if you want to make a semi conversion mod, basically a new game using Blizzards assets. What may be a more viable option are rebalancing mods, these seem to be especially common for grand strategy games. They do require some sort of coding though, but they can be a fairly simple way for a designer to showcase themselves.
I wouldn't personally use game design courses to base what you should or should not be showing/doing. That is primarily because they are academic and as a result they focus on the research/theory side of games. That is if they aren't really programming/art courses masquerading as game design courses. Although valuable in some respects I can't see most Indie teams seeing the value in your 5000 word essay on the apparent use of game theory and behavioural psychology in a modern RTS.
Previously completed projects especially caused a huge boost in interest -- "finally, a chance to work with someone who can definitely finish a project!" -- as they show an increased chance that all the developers efforts won't simply be wasted.
That is so true. From personal experience I was always attracted to teams/leads that had at least some complete project under their belt. When joining a team it seemed to play less of a part though, in those cases it wasn't to much completed projects, but examples of work (even from uncompleted games). I was never attempting to join a group as a designer though.
It is almost always the case that a game developer, or indie team, is full of ideas that they want to realize but requires a lot of programming work. However, it is almost never the case that there are excess software lying around waiting for game design ideas. The bottleneck is always the programming.
There is definitely an issue with supply and demand. I'm not sure if its actually real, i.e. there really are less actual programmers than actual designers, or if we just perceive it that way, in part because of the large number of "fake" designers (if it's even possible to make the distinction). It certainly seems to result in a world were amateur designers feel they have to go above and beyond to prove themselves. Although I can't help but feel that's also in part down to people viewing them as an "ideas man" and how (at least western) society values those people.
A similar thing also happens with 3D modellers/artists with heavy conversion mods. I.e. an apparent lack of artists compared to the number of projects needing them.