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Peugeot carbolite

I have a 1980s carbolite road bike which I cycled when I was a child. It’s about the correct size for an 11 year old boy so I have given it to my son. I live in the hilly Derbyshire Dales/Peak District border and he finds the original 5 speed maillard cassette a bit too hard going.
I purchased a new rear wheel with a slightly bigger hub - 135 compared to 125 (I think) and cold set the rear dropouts to accept it and a new 7 speed Shimano mega range screw on cassette. I lengthened the chain a little.
The largest 32t sprocket now makes cycling a lot easier for him.
The problem is that the rear derailleur cage sits worryingly close to the 31t sprocket. It won’t change up at all when on the 53 chain ring - but in truth he never used this anyway.
To change up on the small (48t?) chainring to the 32t sprocket he has to hold down the right friction shifter fairly assertively for a few seconds.
I was wondering if there was any easy way of creating some space between the rear derailleur cage and the largest sprocket.
If there were a ‘b’ adjustment I could move the derailleur backwards a little but the simplex derailleur doesn’t have one - as far as I’m aware.
I was wondering about a hanger extender or a longer cage. Any opinions if this would fix the issue or anything else I could do?

Thanks in advance.

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