Whilst recessing the bridge would get your problem solved, I'd say you can go for a less drastic solution. You bridge studs are still a good 2-3mm above the guitar top, and could easily be sunk flush with the surface, either by counter boring the top of the guitar, or by turning the shoulder off the stud in a lathe. I think if you did that, you would bring the action down into perfectly acceptable range, and save yourself the aggravation of routing a slot, and touching up the poly finish.
Also, check neck relief and adjust the trussrod first - my Les Paul had action well over 2.5mm at the 12th fret with the bridge bottomed out when I first strung it up. I was gutted, and convinced I'd bodged the angle somehow, until I checked the relief. My (flatsawn mahogany) neck had bowed like crazy under string tension, but a tweak of the trussrod later, and it was all fine. I ended up having to raise the bridge as the action was too low to dig into. The neck hasn't needed adjustment since.