I don't know if I understand your question, but will try an answer it.
Assuming you allready/going to freeze a stock. Then what ever price you froze it at, and more importantly what the position is valued at, will be transfered into the new stock when it is unfrozen.
Example: Let say you Picked Stock A as one of your 6 picks. Two week later you froze stock A after it went up 50%. A week Later You See Stock B that gets you all excited you unfreeze stock A and Put into Stock B. A Transaction is then used.
Now I will show this examples in Numbers.
Assuming each one of your pick 6 started with an Imaginary $1,000.00.
Lets Say you freeze Stock A when it up 50%. You would now have an imaginary $1,500.00. When you unfreeze Stock A to buy stock B you will get an imaginary $1,500 worth of stock B.
What happen to stock A after you freeze it is irrelvant. And whether you pick up stock B the day after you freeze stock A or three weeks after the process will still be the same. Did I answer your question.