I might be wrong, but I believe I read that, starting next year, Regional Chairman award winner's essays will be posted on usfirst.org. This might be an incentive for submitting teams to evaluate their claims before submitting.
From a team's vantage point, the best way to demonstrate impact is through documentation. Take lots of pictures and get written feedback. Make scrapbooks of events, news items, flyers, etc. Leave the notebooks in your pit area and allow other teams to look through them.
If a regional is local, invite FLL and FTC teams that you mentored and give them a tour of your pit. (I gave a tour to an FLL team last year and it turned out to be one of my favorite parts of the regional!)
Judges also can talk to rookies that older teams mentor and ask about level of support.
Edit: Here is the post that mentions posting essays on usfirst.org:
http://www.chiefdelphi.com/forums/sh...6&postcount=12