Theory: as someone who has run Internet brands in multiple businesses, some thoughts:
1- whatever you choose, don't lose a brand. You've created an incredible brand with DominionStrategy.com. You are easy to find on Google (especially with all the content generated from the form). And I'll bet you have a ton of direct type-in traffic. It's not worth losing by changing the name. Building a brand is a combination of a lot of work, time, and not a small amount of luck. Don't give it up voluntarily.
2- No reason you couldn't build out something like BoardGameStrategy.com. It could be done a few ways:
a- it could just be a dis-aggregation site. The homepage could just have three links: to DS.com, TS.com, IT.com.
b- it could be a hub for everything. Create a feed of the content for. The other three sites (just excerpts of articles with the ability to click through. You don't want to confuse google with duplicate content)
c- I don't know how successful TS.com is. If its not doing awesome the way DS is, you could roll it and an IT into it, but keep DS.com as a separate site.
d- you can always treat DS.com as the brand and grow it away from just Dominon. You are right that it could hurt new visitors who are interested in other games. It's always a trade-off with descriptive brands - but not a reason to abandon the brand (hotels.com is a good example)
e- if you make the look and feel seemless you might be able to get the best of both worlds. Imagine if you had bgs.com with the three links. When you clicked on one you were brought to say DS.com. But the top mastication bar and the colors stay the same. You can easily click over to TS.com, etc. but you are still sitting on the domain name, DS.com. )same for the other sites). The forum is a little more complicated, but you can just set the child boards to take you to the other sites forums. Or live with the fact that all the forums are sitting on DS.com.
The advantage of the latter is that the link equity you have build with f.dS.com can help the other brands get started. You definitely don't want to move the F.DS though. A re-direct will hurt your page rank equity significantly.
Hope that's helpful.
If you ever want to chat about it , let me know. I live this stuff everyday.
Ed