Are Lycoming O-360-A4M engines generally known to have right magneto issues at low power settings?

TLDR - I am renting a PA-28 181 (engine Lycoming O-360-A4M), and have noticed that the right mag is rough at low power settings. During before takeoff power checks, both magnetos operate as expected, but when making dead cut checks both after start and prior to shut down, the right mag consistently runs rougher than the left - is this normal behaviour?

CONTEXT - I've been told, by the club that I am renting this aircraft from, that the engine has always been like this, and that it is characteristic behaviour, but I've been becoming a bit more dubious as the problem seems to be worsening, and I will now often get backfires and VERY rough running (600-900 rpm) on the right mag during dead cut checks. The left mag runs perfectly smoothly during dead cut checks at about 1100 rpm (I conduct dead cut checks with the engine at 1200 rpm for reference). The engine also seems very reluctant to settle at 1200 rpm before power checks are conducted, and consistently jumps between running fast at 1500 rpm and then running unevenly at about 900 rpm. After power checks are made, the problem seems to rectify itself, and the engine will happily run at 1200 rpm.

FIXES - I can't find anything in the POH with this set of symptoms, and dead cut checks do not specify maximum rpm drops / tolerances (although for reference, I can tell you that it is uncomfortable sitting in the plane when the right mag is isolated during dead cut checks). Carb heat issues can be largely ruled out, since I always check this on the ground. Fouling seems unlikely given that the plane is always leaned for taxi, usually leaned at cruise, never flown especially high, and never flown or taxied at low power settings for extended periods (it flies out of a small airport, and off block to take off time is never more than 5 minutes).

I've mostly flown the PA-28 161 rather than 181, and have not flown enough different airfames of this type to know if this kind of anomaly is harmful or not, although another pilot not from this club has expressed concerns. I would much appreciate any advice!