The Browning stocks won't fit right, the Model 11 and A5 have a different angle to the tang, compare your A5 in picture 6 to the Model 11. Give this guy a call and he will have the stock for you,
http://www.gun-parts.com/index.html/ Me personally I wouldn't reblue that gun, I like the patina. I would clean it up good though and put a new stock on it, it looks like your forearm is in good shape so I'd leave that. It is important though on these guns to keep the magazine cap screw tight, tighten it as tight as you possibly can with your fingers.
Taking the gun completely apart and putting it back together isn't that hard if you are mehcanically inclined and have a knack for how things work. If you were somewhat close to me I'd be more than happy to help you out. The Model 11 has a fiber buffer in the back of the receiver which tends to break, disentigrate over the years or just get oily and collect dirt. Mine was in good shape but was oil soaked so I replaced mine with a 95A urethane buffer I made and put in, the original buffer is held in place by a blind rivet.
Parts interchange are hit and miss with the new A5's and the old Model 11's. Some screws don't interchange and on the some of the 20's the bronze bushing for the recoil spring won't work from the new A5's. My 20 also has a flat (square) spring for the recoil spring and the new ones don't fit my magazine tube so I have to buy the old ones. Parts are still available if you need them though. The Savage 720, Model 11 and A5 all have some parts that will interchange as they were all JMB's design.
I would say your gun was made in the last years, all my data goes to is 1944 and the last serial number is 716,840, they were made until 1947 though, assuming it is a 12ga. The choke looks like a Polychoke but it looks like someoen changed the bead to a ramp. Take a look at your Browning and see what I mean. I would say someone added that choke as well, most of them came with Cutts or Weaver chokes.
Do you have any pictures of your Browning A5? I'd love to see more of that one as well.