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to keep the vertical chord of these large diameter wheels in line with the undercarriage legs,so that when the gear was retracted into the wing it would present the smallest possible depth within the wing.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)

I'm sure you're correct Springer. It also occurred to me that it would have a marked toe-out angle with the tail down. This would make it difficult to steer & explain Mark Hanna's comments on unpredictable behaviour after landing.
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Also interesting to note that the 109 had no adjustable rudder trim. They seem to have relied on the brakes for steering & to get the tail up on take-off. Do that in a similar fighter & you would stand it on its nose.

Hagar ,

One possible solution for the 109 might have been to reduce wheel diameter ( possibly lengthening u/c legs slightly to maintain prop ground clearance) and to apply a positive wheel camber. Wing bulges could then accomodate the tips of the wheels in much the same manner as the earlier Spits. I don't think that the aerodynamic penalties of such a mod would have been too great.

We forget though that this was war and so what if you lost a few pilots and machines in landing accidents, the disruption to production of major u/c mods would have been worse.

The Brits for example continued to use the Seafire for carrier work for lack of anything better even though the Supermarine fighter was not  really strong enough for the job. They nosed in so many aircraft on carriers at Salerno due to a lack of headwinds that they had to resort to sawing 6 inches off the prop tips to keep aircraft in service.