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Yes, the side-by-side arrangement was the one I meant by horizontal. I hadn’t thought about weakening the door like that so thanks for the warning!
This alternative has an 82mm backset which might be a compromise:
https://www.periodpropertystore.co.uk/ironmongery-c4/door-furniture-c22/mortice-locks-c25/imperial-locks-g5000-5-lever-mortice-sashlock-p5378It’s an old’ish house and for whatever reason in my mind a handle doesn’t look appropriate.
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This alternative has an 82mm backset which might be a compromise:
With a case depth of 101mm. How will that suit the dimensions of the stile and centre rail, considering there's probably going to be some damage done deeper than the case depth.
Filling the holes left for the original key and spindle will probably be a bit awkward and the plugs may come out due movement in the future.
When you say horizontal sashlock are you referring to the ones where the keyhole and hand sit next to each other? As far as I know this is the only way you get the clearance on the handle you're after.
I would point out though that by moving the lock in the way you are suggesting you will be taking out a lot of the remaining tenon that holds the door together. The result of this will be a substantial weakening of the door.