This sort of serenade and presentation of a rose is a great opportunity for your guys to get more comfortable making public gestures towards women. I'd really work on getting the guys to play along here. It's not a marriage proposal after all! And even if they flub it, the girls will be moving on to the next house and it will be over in a minute. Move the girls to the back of the crowd for this one (ask them to consider it giving the guys a good life lesson) and let the guys move outside their comfort zone for just a minute.

Regarding the 3-way socials, I think that's a great idea if you can get anyone to play along. Attending both the sorority and fraternity philanthropy events is a great way to start, and depending on your campus and the kinds of events, can be the "not to be missed" on campus kind of events. Have as many members show up as possible, dressed for success, in letters, and ready to jump in and play along.

Also, there's a term in business called an elevator pitch. It's a sales pitch that can be shared in total in the time it takes to ride an elevator. Every one of your members, including the most shy, should be able to explain your organization in 30 seconds. It takes a lot of practice to get right, but it has multiple levels of benefits, not the least of which is getting more comfortable talking with strangers.

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I was in a co-ed fraternity on campus during college. We did socials with other groups, a semi formal, and a formal. Sometimes we did socials with other co-ed groups on campus, but we were 90% female (there were about 60 girls and 6 guys in our group at one time) so we also we also were able to plan socials with IFC groups without it being awkward. We also partnered with IFC and NPC groups for homecoming, their philanthropy events, and our philanthropy event. :)

The yellow roses are a great idea though. On a side note, freeze pops are yummy! Unless we are wearing white. ;)

Good point. Even I often settle for a very short and generally unfaltering explanation of my fraternity when I am put on the spot. I generally assume that the the other person only has a polite interest. So I spare them the details and say something dismissive like "The co-ed one" or "the weird one".
People largely don't know much about us so rumors fill the information vacuum. The best one I have heard is that we have a "Hall of Swords". I have never* had a negative reaction when someone learns what fraternity I am in, but a few of my brothers complain that they have.

* excluding reactions that are anti-greek in general

Why do you assume that people are only expressing a polite interest? Also I wouldn't say the "weird one." If it comes out that a member is using that kind of language to describe their own fraternity, then they will wonder why and that makes things worst. You should highlight the unique aspects of your fraternity, both at the international level and locally.

Most people are very surprised that I am Greek. When I off handedly mention the phrase "my fraternity" they say "what fraternity are you in!".

Lately I have stopped saying "the weird one". When I used to say it, it was with a big smile and a laugh, but even so it can give a bad impression. I could talk someone's ear off with a serious explanation. I will stick to more serious responses in the future, but keep them brief.