Shooting technical advice
Like you, I don’t like the idea of a stock being lengthened to the degree you mention with a lump of plastic.
However, I am afraid that a custom stock price seems to be a minimum of £500, plus the cost of the wood, so I suggest this is an impractical way forward.
You could finish up with a stock that is worth more than your gun.
One way would be to get the stock lengthened with wood. A good stocker should be able to do this, and match the grain and colour reasonably well.
I’m not suggesting you wouldn’t be able to see the join, but it would look a whole lot better than a couple of inches of plastic.