1stmar, if you get a standard 100-yard smallbore target, it has an 8" bullseye; that's 4 MOA subtention. And a lot easier to see than a 6" one.
On your M1A's rear sight, it probably has the standard service aperture of about .070". A smaller aperature would make both the front sight and bullseye appear larger and look like they're better focused. National Match sights had either a .0595" or .0520" diameter aperature. And some were modified to have even smaller ones. While the smaller the aperture is, the darker the image seen through it is but most folks can handle one as small as .0450" even on cloudy days.
One method used by some service rifle competitors on their M1 and M14/M1A standard service rear sights was as follows. Clean the rear sight aperture good with naptha or alcohol, let it dry, then pack Devcon plastic steel in it from the front. After it's set, smooth of the front and back surfaces even with the aperture front and back surfaces. Then use a countersink to deepen and bevel the front of it back to where the countersink tip just starts through the back surface. Use a .040" drill bit to carefully drill a hole that size from the front; to all the way through. Use a q-tip to remove any fuzzy stuff around the hole. Finally, color it black on both sides with a Magic Marker.
Go outside and check it out for visibility on the target. If it's too dark, redrill the hole out to .0450" and try again. You'll probably like what you see and notice that it's a lot easier to get precise alignment with the front sight on the target.
Use a 6-o'clock hold; set the black bullseye so it appears sitting atop the post and appears to just touch it. This gives the best vertical repeatability as well as windage.