Here Comes Team Rocket! question

[Hoyas]

Here Comes Team Rocket! (Team Rocket 71/82) says:

"Each player plays with his or her Prize cards face up for the rest of the game."

What happens if I play this card and then use effects that replace those face up prizes with new cards? For example if I use Rattata (Team Rocket 66)'s Trickery pokemon power or play Imposter Professor Oak's invention (Neo Destiny 94) are the new prize cards then played face up or face down?

 

[BJJ763]

The Classic Compendium has some answers:

Q. If "Here Comes Team Rocket" turns all prizes face-up, then if you use Rattata's "Trickery" (Rattata from Team Rocket Expansion) does the new prize card go face-up or face-down? (My guess is face-up).
A. Face up as you are switching the cards. (Oct 5, 2000 WotC Chat, Q9)

Q. If you use the Trainer, Here Comes Team Rocket, then you use the Team Rocket Ratatta's Pokémon Power, would you switch your prize, then the top card of your deck would be face up or facedown?
A. Does it matter? Your opponent will know what you're putting there anyway? For the record though, put the Trainer face down on top of your deck. (April 27, 2000 WotC Chat Q126)

* The Here Comes Team Rocket trainer does NOT permanently change a game rule as previously understood. It has each player flip over all of their prize cards to face up. If a subsequent effect states place a prize card face down, then you place that prize card face down. If an effect (like Rattata's Trickery) has you trade a prize card and does NOT state to place it face down, then you put the new prize card out in the same state as the old one. (Mar 14, 2002 WotC Rules Team Update, Q3)

Imposter Professor Oak's Invention has the clause "without looking at them". The only way to do that is to put the Prize Cards face down.