I think it may be time for a new frame...

[Ming the Merciless]

The frame currently needs to be opened out about 3-4mm to put the wheel in. Theoretically a shorter axle and a shorter spacer on the non-drive side would resolve the problem, but wouldn't that mean the wheel was no longer central to the axle?

Wheel not dished properly then? Plus you need to cold set the frame, assuming steel, it is easy to do. The length of the axle should not effect that, the ends of the axle each side, should sit inside the dropouts, not extend beyond like in the days of nuts.

 

[Ajax Bay]

You aiui are trying to squeeze a 130mm OLN axle into the dropouts designed for a 126mm axle.
This results in both chainstays bending and remaining under stress. The strain may not be equal if one chain stay is weaker.
Both the frames described as replacements sound as if they are 130.
Some measuring seems required.
You've suggested removing an axle spacer. This may need a QR skewer for a 126 axle (as opposed to the current 130).
Then the wheel would need dishing (by 2mm more) and this might mean a weaker wheel than I'd use for touring.
Another approach is to revert to a 6sp block and freewheel (different wheel) suitable for the frame.
Why is the 11t sprocket wearing out before any others? Sounds as if your large(st) chainring is way too small.
Because you're squeezing this 'too wide' rear axle in, the chainline is shifted 2mm at rear. And this combined with overuse of the smallest sprocket is thus increasing (smaller) sprocket wear. For consideration (am assuming an ST BB) use a BB with a longer axle (+4mm) to shift the rings out, first checking that the FD would reach out that extra 2mm. This is a smaller issue than the rest.

 

[Mike Ayling]

You aiui are trying to squeeze a 130mm OLN axle into the dropouts designed for a 126mm axle.
This results in both chainstays bending and remaining under stress. The strain may not be equal if one chain stay is weaker.
Both the frames described as replacements sound as if they are 130.
Some measuring seems required.
You've suggested removing an axle spacer. This may need a QR skewer for a 126 axle (as opposed to the current 130).
Then the wheel would need dishing (by 2mm more) and this might mean a weaker wheel than I'd use for touring.
Another approach is to revert to a 6sp block and freewheel (different wheel) suitable for the frame.
Why is the 11t sprocket wearing out before any others? Sounds as if your large(st) chainring is way too small.

11t sprocket wear, that's was my first thought!

 

[Elybazza61]

I'd go with the Japanese lugged (Mayata maybe?) if it's a nice as it sounds and will probably be easier to accommodate more 'modern' parts without too much faff.

 

[Illaveago]

I'll take pictures and let you decide. The Japanese one is a very pretty lugged chromoly frame, while the other is from a VSF Fahrradmanufaktur T400; these are chromoly frames have a very good reputation in Germany and are much beloved of hard core adventure cyclists.

Both are almost certainly better than the frame I'm using now, but because of the sentimental value of this frame I'm hesitating.

Rest assured the current frame won't be thrown away; more likely it will be repainted and repurposed in some way, probably as decoration in my flat.

I was going to say keep your old bike and use the replacement.

 

[MontyVeda]

Also, from what we could see, the problem was that the dropouts didn't allow the axle to sit straight at the end point.tug nuts can help compensate for this but only to a point.

unless I'm missing something, tug nuts will compensate to the point of perfect alignment. If the end points of the throat aren't equal then you may only need one to compensate for the discrepancy.