Savage Edge only had one action length and that was enough for a full length cartridge. I bet you don't have to stroke the action all the way back for a .223, now do you? Point being, it's a long action type action. It is like my bigger rifle as far as putting a scope on it goes.

This is the back view of 2 rifles with the butt plate set up equal. The two stock's length and drop are the same --
but the scopes are not.
You will notice below that both scopes are backed up all the way that they can go with the front ring hitting the front bell (I have neck and shoulder problems and I need an "upright" head position as I cannot "get down into the scope" any more at all.

How do my scopes manage to work and get back far enough for me to use? The big scope is a foot and a half long (gives lots of reach back and you notice that I use it all -- with keeping 3.5 inches of eye relief at max magnification as I don't like scope brow bruises or cuts when using the high magnifications (been there, done that -- it hurts and it really messes up a set of glasses).
It also has a rubber lip on the eye bell as somebody got whacked by it and they changed the eye bell to make it more brow whacking friendly.
The little scope on the little gun has extended eye relief (nearly six inches worth, with 4 inches remaining at highest magnification). It is a cheap Simmons scope and I have two of them so one can be getting fixed for $10 while the other one does rifle duty. Not the best scope in the world, but it has independently focusable front and end bells which my poor old eyes require.
You can buy these long eye relief Simmons cheapie scopes for less than $50 on the internet.Me, I'd change the scope again to a long eye relief model -- or I would look for a Weaver mount that would let you move the front ring back over the action some. I hate the way that "hanging out over the action" stuff looks though, so I'd go the bigger scope route (or an extended eye relief scope if you wanted the scope to be all short and neat looking).
Shotgun scopes as a class all have extended eye relief and they tend to be small and neat looking scopes. Lots of longer main rifle scopes have very long eye relief (all the Simmons scopes do).
As you have learned from taking it apart, your first thought of shortening the stock turns into a bit of kerfluffle as the tapered plastic and rubber parts all fit together at the stock length and nowhere else.
You can cut the plastic stock and epoxy a normal butt plate on to the gun, or cut all the stuff off your existing plate, sand the inside flat and epoxy that on to the cut off stock (after trimming the OD profile back to fit the cut off stock). Lotsa lotsa work, that.
You could buy (or swap for) a youth stock, which is available for your gun. Bet it doesn't feel right for your adult body -- go to a gun store and try one out for feel as it costs nothing and answers your question on youth stocks for you right quick like.
Good luck with your choices, but remember your problem isn't the stock -- it is really the scope and mount position.