Sounds like a run-of-the-mill 603 upper. The rebated lug is a throwback to earlier rifles but works normally with modern pins.
Without seeing it, it's hard to determine how much "wobble" the rifle has or if it's abnormal. Many (most?) old ARs have less-than-tight upper-to-lower fit but it's not a critical factor to accuracy. Remember that your bolt locks into the barrel extension lugs, creating a relatively solid firing platform regardless of whether the upper and lower are "tight" or not. And with the sights also fixed on that same solid firing platform (unlike, say, an FAL, where the rear sight is on the lower receiver and the front sight is connected by the barrel to the upper receiver), your mechanical accuracy is all in the upper assembly.
I point this out only because you might be disappointed if you tighten up the receiver fit and still not get "decent groups."
Accuracy is going to be more likely limited by the quality of the barrel. (I assume the retro upper came with a retro barrel.)
Some old surplus barrels are simply shot out. Some may have rough bores. Some may have a damaged crown or flash hider. Remember, you're not dealing with a factory-fresh barrel.
Plus, you don't say what you mean by "not decent" groups. Unlike a quality barrel today, which may very well be capable of half-inch groups at 100 yards, even a good condition retro barrel will probably deliver something closer to 3 or 4" groups--and that's assuming that you're doing your part.
Having said all that, if you want a tighter upper-to-lower fit, order a full-fence lower from Nodak Spud. NDS receivers are purposefully manufactured to fit tighter than most production receivers, the quality is excellent, and it'll look "right" on your 603 upper.
Good luck, and post pics!
ETA: Sorry--you posted pics while I was typing! Consider the Nodak partial-fence lower. It'll look great!