ScottS2,
A few things:
You mentioned the thumb pushing off the top card - this actually has more to do with which kind of deal you're simulating than "covering" the bottom deal. A strike deal means the thumb stays "dead" and the card is drug out from under it. In most cases the thumb pushes off the top card to help the other hand take it - thus a "push off."
Obviously your thumb should mimic your thumb when you deal naturally.
Hand and wrist movement - A common tendency in people who are just starting to work on the false deals is to "cover" the action by moving the hands, wrists, and arms. In reality this flailing draws the eye much more than a frozen hand. I would again recommend you study the way you normally deal cards and mimic that action. Most often the deck hand is relatively stationary and the dealing hand does all of the work.
Final thoughts -
For those of you who are working on false deals or are interested in them, keep in mind that these sleights aren't easy. They don't come quickly and they require a high level of attention to detail in order to perfect. I would recommend finding them in print, playing more card games (to study true deals and learn their actual application), and finally, having a concrete need. Learning to deal "machine-gun" seconds or bottoms is basically useless in the real world. Many people mistake this skill as overly valuable in the beginning ( things like rhythm, speed, etc.) and don't study what they're actually used for until bad habits have already been acquired.
If you have more questions feel free to ask.
Warm Regards and all of the best luck,
Edward