A couple of random thoughts:

• If you have a game concept/design and would like to assemble a team to build it, your worth is shown in the draw exhibited by you concept/design. For the purposes of finding people, your worth is augmented by your connections.
  
  Ultimately, if you have the concept, and you have the design, and you're building the team, then it seems like you're not the one who would need to demonstrate your worth. I'm not envisioning someone thinking, "I'd like to work on that project, but I'm not sure the designer is bringing enough value per body to the mix."
  
  Demonstrating value as a designer seems more like something to worry about when you want to get hired. With that in mind...
   
• If you don't have a body of work to show, then you aren't likely to get hired as "game designer". Level design is a much more realistic goal for breaking in. As I have posted in a previous topic, the primary skill you need to demonstrate for that position is the ability to execute a design concept within given constraints. So level/scenario construction is the more relevant skill, especially if you can show how your examples support a story arc, and deliver on various design goals.
   
• Keep in mind that, for legal reasons, existing teams do not want to see your game designs. And if they do hire you, they'll generally own any design you show them.
   
• While being an engineer implies some attributes which happen to be invaluable in a designer - as an engineer, I do not have all the talents of a good game designer. If you do, then allow me to apologize, on behalf of engineering, for any lack of respect for your skills conveyed by the more sophomoric members of our fraternity.
  
  Everyone seems to think they can design games, and engineers who are particularly proud of themselves for tackling a very challenging trade, are clearly not immune to this sentiment.

If you really think that potential contributors might pass your project by, for lack of respect for your past accomplishments, then maybe you could start by focusing on a person or two who you think would have the draw that you don't.

Best of luck to you.

Creating levels in a game editor and going for level design positions seem to be the most direct route to get a design esq role (and then moving to the position of game designer at a later stage). Having said that I don't think they're the best way to show off game design skills. They're more showing that you could design to a brief.

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.