I'm sure that you are absolutely correct about the negative camber of the wheels giving rise to the ground stability problems.It seems obvious now that you have pointed it out.
The reason the designers gave it this camber was obviously to keep the vertical chord of these large diameter wheels in line with the undercarriage legs,so that when the gear was retracted into the wing it would present the smallest possible depth within the wing.
( I am not clever enough to attach an illustration, but I'm sure you know what I mean).
This would also account for the wheels/tyres having to be so narrow.
If you look at a cutaway drawing of the 109 wing, the gear is towards the front edge, forward of the main spar and when retracted the tyres are sitting not too far from the leading edge at a shallow part of the already thin wing. Trouble is there isn't anywhere else in a 109 wing for the undercarriage to go.
I think that to change the basic undercarriage design would probably have required a complete re-design of the wing, something that could not be contemplated in German wartime industry.
By contrast in the Spitfire (also with a shallow wing, but of greater area than the 109 ) the chassis ,whilst still hinged at the fuselage end ,retracts into the thickest part of the wing , behind the main spar. This allowed Supermarine designers to give the wheels a positive camber and fatter tyres albeit on smaller wheels.
Willie Messerschmitt must have been aware of the problem from an early stage, because in the bf 108 Taifun with a similar basic chassis to the 109 (but hinged at the wing root rather than the fuselage) he was able to give the wheels a slight positive camber because of the thicker profile wing.
The proposed 109 replacement the 209II had a wide track inwardly folding chassis with positve camber wheels ( like the FW190 and the Hurricane)