ozymen

when I googled those three phrases, I found that "as a means of" is the most used, "as a means to" is the second and "as a means for" is much less used.

I think OG gave a clear expanation on the differences between "as a means to" and "as a means of".  There are subtal differences in the meaning of "to" and "of".

preposition "to" suggests the meaning of "leading to the results of".  "of" suggests possession relationship of the preceding noun and the succeding noun.