Check out this YouTube video on how to get through that dealing assignment real quick!
The empowering technology here is the Dealing Board which is made from 16-18mm customwood. By placing the lugs of the board on the leading edge of the dealing board the board may be popped open by pressing gently down with the thumbs. The cards are scooped from the end pockets into the middle ones then lifted and (more or less) "thrown" at the two cards taped on the sides of the hopper. About 80% of the time they will fall neatly into the hopper with no further assistance.
Sitting a pile of 8-12 boards on your knee is also very good for time-and-motion workflow. To keep your knees as near horizontal as possible, use a footstool or drop one of those pneumatic office chairs as low as it'll go. Looks funny: works well. Good for the boards too as, being lower, you're more inclined to pull them out of the machine by the base and not the lid although, as you have seen, it is very useful to shake the cards into place by jiggling the lid at times.
The aim of the game is to load the hopper in the time that the machine takes to deal the last board inserted - about 6-7 seconds. On a good run you can be waiting for the machine to finish most of the time. Whip the dealt board out and slap it onto the growing pile then shove the next board in. Cycle can be under 10 seconds - but let's allow 12. Five boards to the minute means 24 boards in under 5 minutes in the best of all possible worlds.
But then there's Real Life usually making its presence felt!