Here's a solution, pull all basics (non-fossils) from the deck and make the player pick one. Then, the player draws six cards and adds the basic picked to his hand. No more need to mulligan.
IMO, a judge CAN'T make a player play a Fossil if he doesn't want to. Nope, the only option here in my book is to either give the penalty OR force a random basic to be put in the starting hand. If there are NO basics in the deck, AND the player continues to mulligan, you penalize. It's that simple.
The violation is simply "game disruption." The penalty can go as fas as giving a game loss, nothing higher. The subjectivity is, how long do you let the mulliganing continue. 3-5 minutes is reasonable in my book. 10 minutes is too long.
Regarding someone's comment about giving a verbal warning before making a ruling, that's important, but not required. At home, I often keep my son "on his toes" by IMMEDIATELY punishing him when he does something wrong, not like my wife who sometimes gives numerous, meaningless warnings. JMO