G'Day Fella's,

Tentman, what I do for additional ring security with parallel dovetails on centrefire rifles, is to drill and tap (one or more blind holes) the rear face of both rings just up from their bottom and place an appropriate sized screw(s) with a large diameter head, in there!
What your trying to achieve here is to use the under hanging screw head, to engage with the rear face of both the Receiver Ring and Receiver Bridge dovetails!

You will need to use some caution with this, so as to not interfere with the dovetail clamping screw of the rings! I usually get the job done with either 4 or 5mm (3/16") diameter, high tensile "Button Head" hex drive screws. The button head have a larger diameter head than most standard screw heads, so are almost made for this task!!!

There are more unobservable and also more drastic ways of achieving this security but the above does not require any modifications to the firearm itself.

Hope that helps

Doh!
Homer