Wow what a great question and a tough one to be sure.
Getting elected to Greek Council could be tough (?) no? If one can, I am sure it would give a little more light to Your Chapter, but how much. Maybe I am just to far removed from Campus to understand.
As for Chapter size, what type of Alum Size do You have and how many are close to the College?
My Chapter has been going through many changes over the last 4 years and was at a low ebb with only one Active and no house. But with the core group of Alums, that has kept it alive, We now have some of the Local Alums getting off of their duffs and getting back into the workings. While amny times, Active Chapters poo poo Alums We can be of great aid.
We started again at a grass roots one on one, Alums helping to promote LXA on Campus at a couple of events, Tailgating at Foot Ball Games with LXA banner present.
Promote Your Fraternity by having Members wear letters instead of beer, or company letters. If they know someone in their classes, envite them over for say a BBQ, Bowling or Horse Shoe get together.
An example is PSE who left Campus and merged with PSK and then reentered campus. Had around 6 members but when you saw them in a group at football games, they were all together and wore their letters. They found a small house to rent and are now # 30 members. It can be done, it will be hard, but again, it can be done.
Good luck if this is Your Chapter.