If you get a bridge pickup with strong magnetic pull , it can affect the string vibration, damping it for one.
It will introduce hum.
Unless you increase the output of the bridge pickup, it will be overwhelmed by the output of the split coil.
Therefore with weaker magnets, you would need more windings, which will have a different tone profile.
A large component of the MM pup is the strong magnets, and large poles, if that is a goal, keep that in mind. Look at M&V pickups.
https://www.mvguitars.com/home-3-1-1-2
Or similar split coil designs
That said, I'm not one to rain on a mod effort, if you are accepting that this mod is a one way street.