Gl Bedding a rifle for higher accuracy?

I have problems with recoil. First, I am very small. Five foot four, 110 pounds. Secondly, I am recovering from surgery. I have a congenital birth defect of a caved in chest (pectus excavatum). It didn't bother me when I was young, and I even got a waiver for it so I could serve in the military. It got to where it was causing me heart problems, so I got the surgery at age 34. People get it normally when they are 12 or 13, but my father was angry about having a late-in-life "oops," baby and couldn't be bothered. Because I got the surgery so late in life, they had to take drastic measures. Normally, they put in one metal strap in your chest to open it up. I now have three large, heavy, painful metal straps in my chest. Any sort of recoil is so painful that I think I may p out. Normally, I would go hunting with a BLR Lever Action rifle in .22-250, but I am going hunting in Texas this year. The mule deer I hunt in the Angeles National Forest right behind Los Angeles are not that big. But I got a big tax return this year. I took a $6,000 pay cut as a teacher this year due to the State of California's finances. Ironically, I got a very large tax return. Because I paid a lot more taxes than I had to, due to the pay cut. So I have the money to go hunting in Texas for Pere David Deer at a hunting ranch. However, Pere David Deer are about 400 pounds, and a 60 grain bullet will not cut it. I need a .243. To cut the recoil, I got an automatic. The action absorbs the recoil. Over the internet, I got a Winchester Model 100 semi automatic carbine that was fired once and put away. The gun needs a lot of work. It has no checkering on the forearm, the stock is three inches too long for me, and the scope is this bizarre thing with "rangefinder," and "widefield," lens. I don't like it. It is a Redfield 2x-7x with all these bells and whistles. Some fad from the 1970's. (The bill of sale in the box is from 1972. I bought the gun from the guy's widow.) Anyway, I fired the gun. Oh Lord. 6 inch groups to 8 inch groups. So I went to this old fart at the range who is considered the authority on everything. I have personally seen this guy (he is 71 ) shoot his .257 Weatherby Magnum into a group of about a nickel at 100 yards. He fired my gun. The best he could do was a five inch group, and this guy is a magnificent shot. He said I needed to a) Put a Leupold Scope on the gun b) Make sure the scope mount is correctly mounted, and c) have the gun "gl bedded." (whatever THAT is). He says if I do that, the gun's groups will shrink in half, probably down to 2 and 1/2 inches. So I sent away for a Leupold 1.5x- 5x scope (I rarely shoot over 100 yards), and the mount for it recommended by Leupold. The old fart gave me the card for a gunsmith who will gl bed the rifle. I ume "gl" means fiberglass. But I wonder if I am simply being taken to the cleaners. First of all, CAN YOU "glass bed" a Winchester Model 100? Secondly, will taking three inches off the stock make the gun inoperable? Third, can ANY gunsmith checker the fore end of a wooden gun stock, or is that a job for a specialist? Also, if you were going to shoot a 400 to 500 pound deer with a .243, what off the shelf cartridges would you use? And do you think that "glass bedding" this rifle would make it shoot any better?