How does a freeze/stop pile work in Canasta?
I think you are over complicating what a "stop" card is. When looking at the rules to draw a card from the discard you will note that you have to include it on a meld on the table. Also it should be noted that the only time you can play a black 3 to the table in the meld is when you are going out so normally if a black 3 is on the top of the draw pile it is impossible for the next person to draw a card.

Also with red three's they should never be in your hand as when you draw them they are immediately placed on the table and a replacement card is drawn.

As for your overall question the only state that matters for the draw pile is if it is frozen from a wild card being discarded and that can be noted by discarding the wild card perpendicular to the other cards there is a visual that it has been frozen.  

If a red 3 is the first card flipped over to start the discard pile at the start of the game it will be frozen just as if a wild card was flipped over.