Have had several days now to think about your reply. Either you are not very bright, and have been snookered by some one who took you on a deal involving a gun, or are the type that tries to take other folks. Nowhere in my post did I mention trying to palm that barrel off on any one. I guess you have the same mentality that I noticed regarding a rifle that had the scope base screws canted severely, one member here, of high repute by the way, suggested that the fellow just take it to a gun show and sell it there, pretty low as far as I am concerned, but that type person is out there, I am sure.
My problem stemmed from a brand new, out of the box weapon, and my question was about how to avoid any further mistakes. I will say this, don't know how folks deal with things where you are from, but for someone to attempt the remedial action you suggested should I try to dump the lemon, they would need to pack their lunch, and bring eight strong friends with body armor on, thus requiring head shots.

I appreciate the info. I did use cutting oil, most probably not enough however. What little I have gleaned from the web states that a chucking reamer cuts on the end only, and as this one was not tapered, feeding it into the hole most likely resulted in a less than straight start.
The other thing that I noticed is, the hole itself was touched on by the reamer less than 50%, more than half of the original finish is still left, leading me to think that the factory hole is far less than truly concentric. Prior to touching the frame I wanted to search out opinions and directions from others that have dealt with this type of problem. Am afraid that my technique was to blame for the scoring of rings inside the hole, most likely I canted the reamer to some degree, leaving the barrel lug looking much like the frame, a series of "bands" where high spots wear on the hinge pin. Looking at the original pin, striations appear where the pin meets the frame itself, indicating high and low spots within the bearing surface of the frame.
Finally got a response from a fellow on the Bellm site, his suggestion was to get an expandable reamer for any subsequent work, which allows full length insertion of the reamer, then by tightening a screw, the reamer can be slightly expanded to true up the opening a little at the time, without the chance of canting the cut.

I have an Encore barrel that has "slop" in the hinge pin hole larger than my other barrels, resulting in rattle when opening and closing. I had purchased Mike Bellm's #1 and #2 oversize hinge pins, the #1 tightened up all but one of the barrels, (7mm Rem. Mag.), but the #2 pin would not go through the barrel lug. I also purchased his #2 reamer, but am afraid that I botched the job on the barrel. Not being a machinist by any stretch, what is the proper method for use of this tool? Before reaming the frame, I need direction. Main problem seemed to be how to perfectly align the reamer with the hole. My first attempt resulted in some pretty severe scoring, leaving marks in the lug, and now the #2 pin fell through with no effort. (For good or ill, I degreased the reamed hole, made up some JB Weld and coated the inside of the hole, then using the original pin lubed up with Imperial Sizing Wax, pushed that in, left it for about 30 minutes, then waxed the #2 pin and drove it through, ggo tight fit on the #2 pin now.) I had placed the barrel in a padded vice, and attempted to turn the reamer through the hole as straight as possible. This is a "chucking" reamer, with a handle attached for use by hand. Any pointers or directions would be greatly appreciated. I have ordered the adjustable reamer to do the frame, but having no pictures or discriptions, am hoping some of the posters here can aid in this endeavor.

Do not intend to sell the weapon. Still own every gun or bow that I have ever bought or inherited over the last 50 years. Still drive a 1983 Toyota 4-wheel drive that I have owned since it was new. Your suggestion that I would try to "pass off" a weapon that I had lessened the quality of is pretty presumptuous for some one who does not know anything about me. You may know folks like that, have some acquaintances that are that way, but I shun such people, and deal with them only when my family's welfare requires it at my job, and then through gritted teeth.

Basically purchased this rifle because I liked the look, and the ability to swap the barrels for different calibers. If anything, I intend to add to the group. Problem is, the rifle as sold does not shoot worth a dime. The first barrel I bought, a .223, would not keep a five shot group in a 2' square. I was ready to send it back for my money, or use it as a stake driver till I found Bellm's site. Pillar bedding the stock, using a #1 pin, and getting the correct headspace improved the weapon tremendously. However, the second barrel I bought, the 7mm. Rem. Mag. had a barrel lug hole that would allow the original pin to slide through, with no bite at all. With the factory pin, or the #1 installed, there was an definite wiggle each time I closed the barrel, could move it from side to side, and that I think is not a good situation. Also, the chamber is cut so deep, that there is .002 difference between the base of R-P factory ammo, and the face of the barrel. W-W is worse, average .003. Belted magnums are supposed to headspace on the face of the belt, but this chamber is cut so that the loaded round sits lower than the face of the barrel. A .005 gap between frame and barrel means there is a big, in my opinion, gap for expansion every time the weapon is fired, nothing in the T/C date references this situation, but on every belted cartridge Encore barrel that I have looked at, there is the same problem.

I am simply trying to make a bad situation better by asking for advice and help from the forum, as the only thing T/C has told me is that my weapon is within their tolerances. I find it fairly pathetic that the frame that came with my first barrel will accept the #2 oversize pin at .438 for both sides, and will take the #3 pin on the right side at .439, when the original pin shipped with the weapon is sized .436. When I talked with t/C about this, all they could do was bad mouth Mike Bellm. Thirty five years ago, T/C make a quality rifle, I still have and hunt with my Hawkin, sad to say, the quality of their modern weapons is not what it once was.