I'm fairly familiar with those programs, having used them on behalf of a 20-person corporation some years ago. They're designed for small organizations, specifically organizations that are too small to have much clout on their own. That means organizations that spend a whole lot less than $5 million a year total, let alone with one airline. (In a good year our total travel spending was in the low six figures.)

I agree with Mwenenzi that you should be able to negotiate much better terms on your own. The discounts you should be able to get will pay for the awards that any of these small business programs would give you many times over. (For a while we were able to use IBM's airline discounts as an IBM supplier, even if we weren't traveling on behalf of IBM, and even if we weren't traveling for business at all, until that supplier benefit stopped. Fares were always heavily discounted, often as low as half of the best we could do otherwise.) It's not points, but the savings will more than pay for whatever you could have used the points for. You can even negotiate status for a few people, perhaps including yourself.