Savage 340A Stock Fit and Glass Bedding

Hello,
I just came into a Savage 340 in .30/30 win. It’s a neat little rifle that seems it could be fast handling and since spitzer type bullets can be used, I think I could get better performance out of the cartridge....I have some questions; maybe someone could help or steer me in the right direction....
Having taken the rifle out of the stock, I see the unusual way it is fastened....there is one receiver screw going into the recoil lug, and the other to a barrel band that pulls the barrel into the channel which seems to free float the receiver.... Just setting the barreled receiver in the stock it will rock on a point behind the recoil lug. Is it supposed to do that??? I was considering glass bedding the recoil lug, about an inch forward that, and the band / nut on the barrel band....Should I consider pillars also? Has anyone done this before???
Next, I was contemplating having the rifle drilled and tapped for a side scope mount. A B Square set came with the rifle but was never installed. Are they any good? Should I just consider an aperture sight (Williams, Lyman) instead? Any information would be greatly appreciated.... Thanks.

Can't really help with the bedding info but might be able to help with the peep sight.

First off, some of the 325's weren't D&T'd for a peep, does yours have the two holes on the left side of the receiver at the rear of the reciever?

If so you can probably find a Savage 175 peep sight at a fair price that will make a good fit. They were a delicate sight and broke often if you don't treat the gears gently so make sure you find one thats complete. I think the Lyman TS might have fit those as well.

Welcome to the 340 club. I have had one for a long time. I think you have to bed the barrel band and the area ahead of the recoil lug. These are the two main areas because there is no tang screw and the wood contact with the tang is very small.

Concretus: I just finished a reply that was a marvel of clarity and thoroughness and couldn't post it because my login time had ended. Now I can't get the text back. Here is a quick summary based on my experience with a 340: I did not use pillars. You should epoxy bed both sides of the barrel band and an inch or two agead of the recoil lug. Try to correct the rocking of the action when you do this. A B-square scope mount has worked well for me with a Bushnell 4-12x variable. If your 340 is not D & T'd for this I would have a gunsmith do the job. Good luck!

I ran across an great little article on the 340 when I was looking for info on my Savage/Springfield 840E. If you haven't already found it, this might get you there. New to posting here and not sure how happy this forum is with off off site posts but here's a try: http://ataleoftwothirties.com/?p=978

If that doesn't work just google "The Savage Model 340: An American Classic".