[Firehouse]

I would think the best role for the alumni would be direct funding, and support in the form of providing an attractive venue for informal socializing. Someone's home can be a very effective place for a small rush party.
I think if your chapter presented a united front and said, "Yes, we want this and we'll support it", then your national office and/or local alumni would fund the project. What you're hiring is a Captain to direct the effort from inside. Your united front tells the alumni and the national office that you're serious about being successful, quickly.
Here's where I caution you: don't do this on the cheap. Money invested here, now, will be richly returned. Offering a woman room & board is not enough. In fact, the best thing your national office may be able to do for you is identify a good candidate. First place to look is a young woman who just left the national staff after a term as chapter consultant. I strongly, strongly suggest that she NOT be from your chapter. And again, this should not be someone who comes to graduate school on your campus, and takes this responsibility for room & board. No distractions. She is a full time soldier of fortune for a year. What does she get out of it? She gets a unique resume item ("I was chosen by name and recruited as a paid executive to rebuild a collegiate organization from scratch. I operated independently, managed the budget, organized the volunteers, and achieved all of my stated goals. I am the only one ever chosen for this distinction."). She also gets cash, which everyone likes. Finally, she becomes a legend, and the value of that is hard to measure. She will need to be strong, visionary and be self-motivated. What a fantastic opportunity for some very lucky Chi Omega!