MIJ SD Shallow pickup height?

[The Rossness]

I've got a MIJ Wildcard primer model San Dimas (the guitar in my avatar). For the longest time, I left it stock. Finally I started playing around with new bridge pickups. But no matter what pickup I put in the guitar, it sits too close to the strings and things just sound shrill. I can raise the floyd but my action goes to hell. I've messed around with the tension on the floyd and have it bent forward a little and that's helped things a tad (the strings are slightly raised), but the pickup still sits a little too high. I think the pickup cavity was drilled too shallow. Has anyone routed the bridge cavity deeper in one of these? Is it worth it to route the body, or should I just get a MIM body off ebay, keep the neck/ pickups/ hardware and sell the original body?. What's the scoop?

[Coolidge]

What is the pickup height measured from top of pup to bottom of strings? With the string fretted at or near the highest fret it should measure .060 to .090 inch on the 1st string and .125 to .150 inch on the 6th (bass) string.

[DonP]

You can try getting short leg pickups.

If it's only a small amount, raise the Floyd and Shim the neck to get the right action. You would shim it on the body end.

[The Rossness]

I havent measured. A jb fits but not much else (it was the original pickup) short legs don't make a difference, the pickup still sits too high. I shimed the neck, raised the floyd. Did all the normal stuff. But now the action is too high. I did read a thread about some of the MIJ SD’s having shallow pickup routes and it got me thinking. So, what do I do? Buy a new body or try to route the cavity deeper?

[Adieu]

I know DiMarzio has multiple pickup "heights", including some pretty tiny ones