On a lesser level (i.e. not "challenging for national prominence" but merely examples of 1-2 elite individuals being the difference), a few teams that I saw personally include the 2006 Carnegie Mellon and then 2007-09 Case Western teams. The bulk of 2006 Carnegie Mellon's roster was likely not much different than the teams that came before or after it, but in 2006 they had the program's 1st and 3rd all-time leading rushers in the same backfield. Take those two dudes off the team, and instead of 11-1/playoffs they're back to the same 5-5ish teams that came before and after. Ditto Case Western and Dan Whalen, who lifted Case from a 5-5ish program to three straight playoff appearances, after which they returned to the same .500-ish level within a few seasons. Those are just examples I remember offhand, no doubt people more familiar with the various leagues can list some other similar individual/team examples. Scottie Williams at Elmhurst is another that comes to mind. 2012 Elmhurst, with Williams running the ball, goes 10-2 and gives a legitimate challenge to Stagg Bowl finalist UST. The Elmhurst teams before/after that were basically .500 teams. In Division III, perhaps even moreso than Division I, the difference between being a middle-of-the-pack team and a fringe-level Top 25 team often seems to be the presence of one or two truly elite individuals. Obviously you still need the roster of supporting players around that guy, but I pretty firmly believe that the "regular guys" on many Division III teams are pretty similar.
What seems to set UWW and Mount (and to a slightly lesser extent UMHB, Wesley, and Linfield) apart is that they have the overall roster depth that 1) the next star-in-waiting is always there and 2) even when he isn't, the rest of their "regular guys" are so good that the team doesn't really drop off much. Most good-but-not-great D3 teams seem to lose a guy of that caliber and don't have the next superstar lined up; they have a team full of "guys" just like they had before the superstar arrived.
Heinsohn at W&L was another great example. He made that triple option go from respectable to devastating. Top 4 in the Gagliardi behind Williams in 2012 as well. Two out of his 3 impact years (played as a frosh, but not like he did later on) W&L won the ODAC. Since then the Generals are struggling to rebuild.
Sometimes in these conferences that are tight, that don't have the behemoth program, it is just that 1 guy. Probably a lot more examples if we looked.