Archie: If you want to get a Rem 7400 or 7600, I fergit which is the pump and which is the auto, you need to do a bit of 'smithin' to get them to shoot more accurately. I've played with a couple of the Rem semi-autos in 06 caliber and they need finessin'.
It's almost all in the front forend. You may need to smooth a trigger a bit if you have a burr but most of the triggers on the Remington semis are pretty good.
In the forend area, there are a couple fo things you need to do (1) make certain the backend of the forestock is square where it mates to the front of the action. Sometimes varnish buildup or poor finishing needs correcting and that end of the forestock should not impact directly on the front of the stock or when it (action/barrel) heats up it will throw your accuracy off. (2) at the front of the forestock/forend, there is a metal end piece, a white spacer, maybe a black spacer and the stock attachment mechanism (screw and base). The metal piece and spacers need to be relieved in the barrel channel so they do not impact directly on the barrel or it will throw off your accuracy as the barrel heats up. This is just like relieving the stock to bed it on a bolt rifle. Also on the semis, the barrel attachement (screw and base) need to be dealt with so that even if you white-knuckle the screw it won't tension the barrel and throw off your accuracy after every shot. You can do this with a small metal washer that allows the screw to bottom out without putting tension on the barrel. (3) You could also bed the forend stock to the barrel in the area of the chamber, but no further down the barrel channel.
After that, you reload to find your most accurate loading. However, on both Remingtons I've worked on, the factory Remington 180 grain 30-06 round nose slugs were as accurate as my best handloads and since they are fairly inexpensive at Wal-Marts and the like, it is easier to to stock up from there than to reload. Be aware though that the Hornaday Light Magnums may not cycle the action of the semi-autos. Hornaday purports to use heaviewr charges of slower burning powders to get the 'light magnum' velocities from bolt guns - those powders won't cycle the actions of the semi-autos.
Hope this helps. Mikey.