I believe the weaver base part number should be 48347.I paid $12 for it . The Weaver quad lock rings you are looking at is right but you most likely will rub the scope when cycling rounds with that ring and base set up.I have that same set up and it works but there are better.EGW 1 piece is suppose to be better because it is thicker but it is $39 for the base through amazon.The last time I just went with the stock 2 piece bases and a set of Burris 1" high Zee rings.part #420087 and that gave me better clearance than the set up your looking at.The Burris rings were $34.00 here locally, I'm sure you can find them cheaper but I recommend those rings over the quad lock.The Vortex sounds like a great scope.I was tempted to buy it so many times but always opted for something else.They make a 2 piece weaver base #209 that was posted here and sets you closer together if I remember correctly. I hope this helps.
Ok I took a few pictures Here is the set up you are looking to get with a different scope of course but you can see the problem once the bolt is pulled back by the scope.It can rub if you push upward as your pulling back.
Then there is the issue of grinding the front ears of the base down if you want to set the scope further back. This is a 40mm scope so I'm not sure you can do it with a Vortex 44mm and still have clearance or not. It might fit but would be too close to call either way without actually trying it.
Here is the last set up. Lots of room with the stock 2 piece base and Burris ring.
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