Well, the most effective way IMHO is to build a sample app displaying the alternative. Then, compare the cost of licensing Access installations, cost of maintaining installation support vs costs in developing and supporting with the alternative. It may not get you what you want in such a small org, but I do think you need to examine what the expertise is at you org, and how much resource you can throw at a conversion from those apps to your proposed alternative.
You may find it's not a cost effective solution given the support/development staff level. We put MS Office, including Access on the desktop, and let the users build their own apps, and support them, as well. I wouldn't have enough time to troubleshoot their stuff or develop alternatives. Although, much of what I use involves .Net, windows apps or web apps, I would not try to convert everyone in the org, becuase it would bring a lot of support calls to me, and I don't have that kind of time.
So, it's a question of Total Cost of Ownership, which includes support costs. If you have to do the support, and queries anyway, you might win, but if the users do them, then, it's probably not going to work out without a lot of effort.