FishNoob wrote,
There are two filters involved here ..........
The old one would be the one that would be running inside the 125
during this procedure, so it would be operating as normal. The other
- the larger filter from the 125 - wouldn't be.

Mabe I'm the one missing something here (?) - if both filters were on
the same tank to start with, the bacteria colony needed for the
bio-load would be split between the two filters. To remove one and let
half the bacteria colony die off, the colony within the other filter
would be under sized, alowing mini spikes of ammonia and nitrites while
the other filter is re-colonising - playing 'catch up' for the next few
weeks. Now, if it were to be placed on the side of a bucket of tank
water, and fed a few drops of pure ammonia every day, for however long,
there wouldn't be any die off of the colony and no need to cycle the
filter again - jmo............ Frank