> So, how many times will parameter shift be required?

Parameter shift will occur whenever a factory's capacity is used up (Fn
times)

So we have Fn shifts of parameters. Every shift of parameters takes
O(Qn) -because every parameter takes the velue of the next parameter.

Therefore, the time only the shift of parameters will require will be
     Fn * O(Qn)

which, of course can be written as:

O(Fn) * O(Qn).

This was my initial estimation and you now confirm it.

A better time complexity can be achieved if the "shift parameters"
operation can be replaced with something else.