When you say the hub is out of true, how do you come to that belief? Are you keeping your eye on the outer edge of the hub itself as it rotates? Or, as is visible on one of mine, is the brake shoe visibly not engaging with part of the inner track?
If you tighten the hub up to the proper torque setting, with the shim under the cone, is there any play if you grab at the hub, other than the normal “give” you get from the rear hub bearing?
Has the hub ever come loose? I ask as I would have thought that if you have an incorrectly matched cone, the hub would move and you may initially feel this by the brake coming on and making the hub hot.
I have seen the outer lip on plenty of my shoes in the past and never thought anything about it. I may be wrong though. The cone on the layshaft, with the hub off, is not especially tight. You can normally take it off with your fingers.
Having asked all these questions

, I do recall reading posts about Scootopia hubs not, at one time about 3 years ago, being a brilliant match with their cones
Since Uni started making hubs several years ago, I have used them without real issue. FA Italia were the generally available ones previously. Uni are much better made, in my opinion. The only issue I have come across with Uni ones is that the inner track does not always engage 100% with the shoe throughout its rotation.