There's crossed wires here I think, or I've got mine crossed 😁.
If the centre block/neck is shimmed then the bridge mounting area at the rear of the centre block will need to be shaved down flush with the body to lower the strings.
I feel this is probably easier than routing the bridge area down to achieve the same, as the routed area will need to be the centre block and the actual body. The bridge mounts solely on the centre block but also sits on the body.
The only 'issue' I see with shimming and shaving is the the centre block won't sit flush with the body anymore (a slight taper to however high the bridge area is before it's shaved down). The entire centre block could be shaved down but that's quite a lot of work.
There's probably no right or wrong way, just whatever you'd prefer to do, including chopping the neck off to make it more conventional and shimming that. Either routing the bridge or shimming and shaving the centre block will work, but the will both have their set backs, like possibly needing to route the pickups lower, which being mounted to both the centre block and body give their own problems.
Personally, as long as I felt competent in doing so I'd just pick a way I felt comfortable with and go for it. Work out the wrinkles along the way, as the bass isn't valuable enough to warrant paying for the work to be done. Whichever way I went I'd put extra fixings in the heel to stop the neck pulling up again.
Whatever you choose to do please keep posting as I'm intrigued to see the solution.