ORIGINAL: Alsatian
TUK101: I once had a scope mounted which moved in the rings. The gunsmith recommended that I put a dot of fingernail polish on the junction of one of the rings and the scope, so that if the scope every moved again I would immediately be able to recognize this problem. Since then I have always put two dots of fingernail polish -- one on the forward edge of the rear ring and one on the rear edge of the rear ring -- so I can tell if any slippage is occuring. This may be good advice for you.
I think the advice people are giving you to lose the see through bases is pretty good advice, but this is a matter of personal preference I suppose. You should definitely be able to get better shooting out of your rifle than 4" groups at 100 yards. My Winchester M70 featherweight .243 shoots 1.25" groups, and I'm pretty sure I'm the limiting factor on this accuracy rather than the rifle. This is good enough shooting to use the rifle out to the limits of its range. The .270 is good for long range, but a 4" group at 100 yards is going to open out pretty quickly at longer ranges. What is going to happen when you take a 300 yard shot on either a deer or a pronghorn antelope with that rifle if it is shooting 4" groups?
Having said this, if you think the scope and scope mounting mechanics are sound, experiment with different ammunition. I have found that shooting different ammunition out of the same gun I can have groups that range from 4" to 1.25". Buy about three different commercial loadings in the appropriate bullet weight for your preferred game and shoot several 5-shot groups with each cartridge. You will probably find that one of these loads makes consistently better groups than others. Use this preferred load. By the way, this is something that is unique to your specific rifle.Just because Acme's SuperBangerBombshell shoots 1.25" groups in my Winchester 670 does not mean it will shoot 1.25" groups in your Winchester 670. Even less would this be the case comparing between my success with a Remington Model 700 BDL in .270 and your success with the same load in your Winchester 670 in .270.
Good luck.
Thanks for the reply, and even more for the good advice. When I said that I was shooting 4" groups, I didnt mean that I was going to just leave it at that. What I meant is that at least finally had it shooting consitantly in the kill zone. I will surely fire more ammo through it and get it dialed in as best as I can. I just had to take a break from shooting for awhile and let my shoulder and neck settle down. I will definatly do the nail polish trick to see if I am getting any movement. The reason for using the taller rings is so that if I jump a buck at 25 yards I can stand a chance at hitting him with the open sites instead of trying to find him in my scope. This happened to my neighbor last week and he ended up missing the deer at 25 yards trying to decipher what he was seeing in the scope that close up. The rings that I am using only have the reticle setting at 1.75 inches compared to the 1-1.25 standard rings do. Thank you for all of your feedback guys, I really appreciate it and look forward to more words of wisdom from all of you who care to share it.