Of all the sound effects in Christmas Carol, the clock tower (Big Ben) is not supposed to be "in frame". It's supposed to be slightly distant.
In my productions, there were only a few sound effects other than music.
One is when all the bells in Scrooge's
house ring for
Marley's entrance, which we did live, because I couldn't get a good enough sound
effect together in time. I and three cast members rang an assortment of
hand bells.
Another being
Marley's chains, but he did those himself.
Lastly the clock, which I used an actual Big Ben sample, and copy/pasted the "hour bell" portion for each different time we needed. (7 - Cratchit leaves the office, 1 - Past, 2 - Present, 3 - Future, 9 - Scrooge waiting for Cratchit) Then I used my sound editor to speed the whole thing up a
bit, because waiting for the 9:00 bell to finish chiming (while the actors are trying to get out their lines) just wasn't working for us.
SO, that's my recommendation, if all other sound effects are done live, and make sense to be done live because they're related directly to objects or action on
stage, then the one
effect that doesn't need to be would be the clock. Unless you don't have the means for the sound effects to go out over a sound
system....
In which case... maybe get the closest church in the area to
play their bells on
cue?