It seems to me that all we will ever be able to say is that this is down to tyre construction. Yes, the manufacturer's choice of tyre size puts us in a non-ideal place to begin with, but some tyres in that size achieve stability on a given chassis and setup, and others don't on the same chassis.
Oh, and I believe tramlining and wanderlust might well be related. If a tyre hits an uneven surface it will either comply well with that surface, achieving practically the same contact patch, or it will not, leading to an uneven contact patch. Whether that causes the vehicle to pull laterally depends on what happens to the contact patch, and how its' interaction with the tread pattern causes the forces that act on the tyre to vary.
It could be that with some tyres, those forces vary through minute variations in the vehicle's steering input and poise, leading to seemingly random changes in direction. With the steering and suspension setup on the Omega already being less than ideal and therefore sensitive to such forces, the result is where we are.
Yes, it would be nice to know in advance if a particular make and model of tyre will be satisfactory, but I can't see us ever achieving that, as it's clearly not down to an advertised aspect of tyre performance, but, I suspect, some subtlety in tread pattern, depth or compliance of the tread area and/or sidewall.
I can't see us getting beyond "suck it and see", to be honest, complicated by the fact that one man's "severe tramlining" is another man's "it does the job".