Well.. there are a few approaches to finding alumni, but I can't guarantee they'll respond, and the best ones (insofar as finding alumni you might not otherwise know about) are very time-consuming.
1) Pull up your chapter's alumni roster on apo.org. If you can, download the tab-delimited file so you can save it in Excel and update it easily. Take that list to the alumni association office in person, tell them what you've said here, and ask them if they have ideas for locating these alumni. After you've exhausted that route, then try to find all the alumni you can.. I worked on a similar project for a chapter last year and was able to find a bunch of people through Facebook, including a former chapter executive from 1950 (yes, on FB!) so anything is possible. I didn't find a paper alumni directory in the USC library database, but you might ask the librarians if such a thing exists as well. If you're feeling very energetic and have help from other chapters, try the same paper-directory idea with any other nearby schools that have them.
2) Ask other alumni for help and contacts. I promise that your chapter knows some. Section staff, your section chair, region staff, advisors for other chapters.. particularly ask Paul from UCLA. If there's anyone I know that would have contacts, it's him. You can also try asking Eddie from UCLA. To get their contacts, login to apo.org and use the chapter lookup tool under chapter resources to find Chi chapter, then click "view details" on the right. Maybe some of the staff/advisors you talk to about this project will be established in various industries themselves, and might be available for the dinner.
3) Ask other chapters for help. They may be in better contact with their alumni. Consider asking every California chapter for help, even, since so many people go to the other side of the state for school.
I don't know how things will go on such short notice.. but good luck! Sorry if this post rambles a lot, I haven't had much sleep.