Just making a suggestion:
First of all, the laws of geirus have to go somewhere. A lot of sugyos in the gemara seem to be based on this principle. For instance, there are many taharos sugyos scattered in lots of places, largely because most taharos masechtos do not have any gemara. They have to go somewhere. You may want to think about this response to your question: where would you put it instead?
That said, I have no doubt that Rav Ashi found the very best place to put things, and that one can understand exactly where everything belongs.
The direct linkage would be the story of Rus, who was a גיורת and who has a yibum in her story. So I guess that's the second-level p'shat: a way to connect the laws of geirus to Yevamos through a common story.
For a third-level p'shat, I'd suggest that the idea of yibum is תיקון, fixing. Yibum is the way for the wife of a "unsuccessful" marriage (that is, with no offspring) to try again to succeed. She doesn't want to go out and find a new husband; she wants to keep this family together, keep this relationship going. Even her husband's death won't stop her.
Rus is the classical example of this never-say-die attitude. Naomi tries to convince her to give up. Rus tells her, Please leave me alone. I don't listen to people who tell me to give up. I'll never leave you, and I'll never give up. I am going to keep this family together.
I think this is why Chazal say that Rus was the forerunner of mashiach. Hashem never gives up either. Israel fails; Hashem finds a way to try again. We set up barriers, he builds ways around them. This is Hashem's decree: In the end, we will be successful - through our own free will - no matter what. (See the Da'as Tevunos by the Ramchal; this is the subject of the whole sefer: how our free will is compatible with the guarantee of our ultimate success.)
Anyhow, I'm thinking that that's why geirus is in Yevamos. Geirus is also a type of תיקון, of people changing themselves to achieve their full potential in Hashem's dominion. Chazal even say that one of the most important purposes of Israel going into golus is that we thereby gain geirim. We actualize those "sparks of holiness" that we find out in exile, sparks that would otherwise have nowhere to go. The nations of the world were offered the chance to be part of Hashem's world when the Torah was given; they turned it down. That needs to be fixed if the whole world is going to take part in Hashem's ultimate kingdom.
Last edited by MichoelR on Mon Jun 10, 2013 2:45 pm; edited 2 times in total