What is the impact of changing the stream cadence?

The way that the Engagement engine works is that the engine checks to see if the lead has or has not received the email in a given cast before it sends, so if you reset the cast like you are suggesting the people that received casts #1 and #2 will receive cast #3 on the new date.  You will only be resetting the cast schedule and not starting the entire program over, to my knowledge. 

Hey Nick, the 'first cast' really only applies to the very first time you want it to go out -- in case you wanted to set it for sometime in the future. Once it's running and you want to make changes, you have to update the date to the first time you want that new time to apply. If you set it today for Mondays, and make the first date 2/29, then there will be no cast on 2/22.

Also, just so that Chris's comment doesn't lead you astray, during every cast the program will look at every item from the top down, and evaluate whether to send or not. So, if someone has received emails #1 & #2, and then you add in a new #1 (be it a replacement, or if you just add another email to the stream,) then the new #1 will be sent to all eligible people at the next cast. The beauty of EPs is that the same email will never be sent more than 1x to a person. That's how EPs are designed to work. So no, they won't receive emails 1 and 2 again as long as they've already received them.