What you seem to be describing is a Remington LTR rifle that has been cleaned up just a bit.
The LTR is similar to the Police PSS rifles and the Synthetic stocked Varmint specials.
They put fluting on a varmint weight barrel which was trimmed to 20" lg. The early LTR's had detachable magazines, but the later ones have BDL style floorplates.
The LTR weighs around 7 pounds without a scope, and will probably go over 8 pounds field ready.
My LTR in particular meets your accuracy criteria with a bit of room to spare. While testing loads I shot four 3 shot groups at 500 yards one quiet evening just before dark. When I went down to check, all the shots except the last shot (which I pulled badly) were in sub-half moa groups. The smallest group went 1 7/8" (remember that they were shot at 500 yards) while the rest were under 2 1/2" but bigger than the smallest group.
Another time a friend and myself were testing loads at 200 yards. We shot about 50 rounds between the two of us. The biggest 3 shot group at 200 yards still went under 1" (1/2 moa) and several of the groups were 3 shots touching.
If you think an LTR might do the trick for you, you can check around and buy one for $700 to $800 new. The local outlet has them for $725 + tax and has several in stock. Send it off to one of the outfits that does good cleanup work such as skim coating the v-block bedded stock, adjusting the trigger, truing up the action, and cleaning up the crown. Do that and the rifle should be set. At that point you should be into it for about $1100.
An alternate possibility is to buy a varmint special (unfluted model) and have the barrel cut down to your desired length. The 20" barrel will give up about 100 fps over the 26" barrel, but I don't have any idea how much would be lost by going shorter.
Get a good bi-pod, scope, rings, & base to finish off the package. I have one of the Springfield Armory 1st gen scopes on mine and have dialed in my handloads to be dead on with the crosshairs out to 600 yards. It makes an outstanding hunting rig. The other way I have seen LTR's set up is with Leupold M3 tactical scopes cause they also compliment LTR's really well and are a bit lighter than my Springfield Armory setup.
[ 08-12-2003: Message edited by: Bruce Gordon ]