What's the OD of the widest part of the objective? Take that, subtract off 1 in/25.4mm for the diameter of the tube, divide the result by 2 and you will have the height you need to clear an imaginary line from the top of the receiver. My guess is that you will be about 0.1-0.2 in short with this measure. Now look at the gap between the imaginary line from the top of the receiver and the barrel. My guess is that you will pick up enough there to just get the scope on.
You can always get the Beeman 5030H rings which have about 0.1" height on the BKLs.
My guess is that the BKLs will be just enough to mount the Scopechief. While they are only about 0.65 inches tall the contour of the barrel and step down from the top of the receiver should make enough space for the objective. Should look pretty nice!
The Millet high CZ rings give almost too much clearance on my American Sporter barrel. Got a set of the Brookie Weaver Low bases on the way and then I'll work out the correct size Burris Signature Z rings.
Seeing how many of us picked up the Scopechief's from Natchez makes me amazed at the influence the good information available here on RFC. Hopefully Brookie and Tony Kidd are doing well with their great products in part because of the influence of RFC.