Low end chainrings are stamped. If any reasonable care is taken when making the die (and it is) the rinfs will all be virtually identical, and the tooth circle concentric with the crank mounting hole. So, in theory, they shouldn't be eccentric, BUT the crank hole is usually oversize to make assembly easier, and so there's some slop that cause eccentricity.

I'd rotate the crank to the point of highest tension, and give the ring a solid shot with a plastic, wooden or rubber mallet at the 3 o'clock position. If the ring moves at all, it will improve the situation, hopefully enough to satisfy you.

BTW- an easy way to confirm eccentricity is to attach a zip tie to a tube and extend it out to the ring at any point, so it just touches the ring at the highest point. Then rotate the ring, and measure the gap at the lowers point.

Lastly I'd be very surprised it there was a total run out of more than 2mm (1mm up and down). That can cause a decent amount of chain sag at the low point, but there's nothing to be concerned over. The shape of the plates and points on the teeth do a decent job keeping in line chains from falling off. In industry, it's very common to have chains that sag like crazy, and they stay on very nicely.