Differential diagnosis via system exclusion. Break things down into large component systems to isolate the general area of the problem, and once that is accomplished continue to isolate and test until the problem is found.
As far as the OP goes, you isolated it to..... a moderator? Or was it simply weight on the end of your barrel? Hard to say. A Dx there could be to hang a couple weights on your Belita and see if the problem returns. A moderator does more than just eat the air coming out the end of your barrel. Aerodynamic interactions can change substantially when things are close together, a moderator can cause substantial POI shift simply because a pellet came to close to an internal surface WITHOUT physically touching it. The weight of a moderator can also change barrel harmonics, among other things. Also were you attaching the moderator directly to the barrel or to the end of the shroud? What if you changed that? Does it change with how tightly you thread your moderator on or its rotational orientation? Ask any Crown owner, they can shoot great groups with their shroud extended, but depending on its rotational position POI will shift without the pellet ever touching anything which is why the Crown shroud has a locator pin so you can get repeatable performance. The barrel/scope rail interface torque is as good a guess as any, and easy to eliminate as a cause I suppose.
I couldn't tell you what was the cause of these issues you're having, clearly, only suggest testing you can do in an attempt to isolate it. *shrug*