slayer, can you obtain any help from your National Housing department and/or whatever you call your chapter support personnel? They may be able to provide you with a timeline, letters, volunteer recruitment tips, and general assistance for fundraising, etc.
You may want to send the initial mailing asking for help and NOT money. Now, hear me out
Let them know that your chapter is currently unhoused, and you would like their assistance to locate a temporary/permanent new housing for the chapter. Let them know what your chapter needs, and ideally wants, in their housing and what they can do to help. Once you make that initial contact, FOLLOW UP. Personal contact makes a world of difference on the alumni level.
Without knowing more details it's hard to give anything but general suggestions, but I hope these help a little. Feel free to PM me if I can help with anything else.