A lot of this alignment has to do with where the threads on each part begin to engage and of course where they come to full stop.
When this happens, it is possible to backfill the original bead hole with a pliable, but firm material that can crush into this hole and at the same time keep the sight secure. This material can take up some of the space and make sure the sight is secured.
Gunsmiths will often shave a tiny piece of lead (Pb) from the tip of a projectile and use this to embed the sight within the threaded bead aperture. This is often successful, but care must be taken, if too much material is used, it can be very difficult to remove once crushed.
For this reason, a gunsmith may be of great value for this replacement and is highly recommended.