In between the traditional shuffles, you could have them fan the cards
and choose a few at random to bury at the bottom.

You could also have them "deal a round" and then
recollect them.  

These would be alternative forms of shuffling.

Here's another idea, not sure how much merit it
has but it is a thought:  After they shuffle several times,
then you have them manually divide the deck into red cards
and black cards and keep shuffling. 

Since most new decks are already arranged by suit, this
separation into red and black wouldn't add any value if
done as the first step...  However, after SOME entropy
is added, you would then be creating a different "starting point",
so you would lock in the entropy generated up to that point
before going on to create additional entropy.

If there was a bad shuffler who failed to create much
changes to , say, the top of the deck, then at least
once you would get a totally new order with this method.