OP - I think go to Brownell's catalogue on-line (website) - they often give a dimension in thousandths of inch from top of scope base to either bottom of scope body or centre of the scope tube - for the various rings that they sell - you will discover that "Low", "Medium" and "High" are words used by most scope ring makers, but many are different heights - a "Low" Weaver is not usually the same height as a "Low" Leupold - and could be different among Leupold STD or what they currently list as "Back Country" - I do not know for sure if there is a difference among those last two - I prefer to work with actual dimension, not words like "Low" or "Medium".
Will also be something to fuss about - length of your scope and the location of that rear sight - I do not think that rear one folds down - so your scope may need to be mounted tall enough to sit above it, or short enough scope to fit behind it - makes difference what OD of your Objective end is - can see various scopes - 56 to 20 mm front lens - really large differences in front objective diameter.
And I do notice in picture on your Post #15 that appears that the rear integral base has been drilled and tapped for scope base hole - to screw a conventional base on top - I presume so has front - so you will need to find bases that fit to that rifle, for the rings that you intend to use, for the scope that you intend to use. I have not seen Warne QD rings for attaching to that rifle's integral scope bases - but maybe they do make them? Might be why previous owner went with the drill and tap thing??
Is another thing - is easily 3 or 4 DOZEN used rings here of various brands, heights and base types - so when dealing with a particular rifle and a particular scope, is not uncommon to try several to see what it is that I want to order. I am not sure that I would know how to do that if I only had that one rifle and one scope here. I had read of ways to "mock up" using modelling clay, wood shims, etc. - to find height (in thousandths of an inch) that would likely work. Is very typical - almost a "rule" - that the rings are same height each other - bases are often different thickness - but when correct, the top face of the bases make a dead flat plane - usually parallel with bore centre line - or slightly tipped forward - but "flat" to each other.