These are kinda random thoughts I had while reading this thread. . .
1. If you've only been in the GLO for 2 semesters, then your big has only been alum for less than 1 year (logically speaking). I would think that it would be OK to speak to her about this, she most likely experienced the beginnings of it while she was still active. (Aside from the fact that I think it's OK to talk to your big about anything!!) My bigger concern is the fact that talking with alums about chapter issues is taboo. Why would you not want their help? Of course, if an alum hasn't been involved in a while, I wouldn't dump everything on their lap. But a chapter who isn't willing to go to some alums for help concerns me. . . (maybe it offends me 'cause I'm an alum who would LOVE to approached to help work out problems!)
2. Every NPC has (or should have) regulations about their chapter's budgets. Especially recruitment budget. Look through you National Constitution/Bylaws and Chapter Handbooks to find the answer. And I agree that you should bring it up privately to the Recrutment Chair first. No need to create additional drama.
3. Do you have some sort of advisory board? You know, alums that advise the exec board positions (Recruitment Advisor, New Member Ed Advisor, Treasurer Advisor, etc.) If so, turn to them for help. Maybe they (or a similar group of alums/advisors, however your GLO is set up) can conduct a 1 day retreat/training, where exec can air their problems/concerns and work towards solutions.
4. You may also want to consider whether or not holding an office in your chapter is right for you. Exec board isn't for everyone. Some of the greatest leaders work behind the scenes in getting things done. They are the assistants and "helpers", and sometimes that is what really makes a chapter great. (Not trying to get you down, but it is a thought!) I would consider that angle before I would consider deactivating. After all, I joined for a lifetime, and while I wasn't the greatest chapter officer in the world, I have found a passion for helping other chapters with the little (and BIG) things that come up (now that I'm alum).

Keep us updated!!