Today, I have had a brain wave and, hopefully, a breakthough...
From the information you kind people have offered, and after ensuring the shoulders were set to their appropriate location, I became even more convinced that my problem reflected a discrepancy between FL die and reamer dimensions.
Assuming my assumption was correct, the answer to my problem appeared to be a customised FL die. However, no such item is available in the UK and therefore I would need to send sample brasses to the USA and then wait for both a die to be made and the subsequent delay for the die to be dispatched to the UK and the further delay of customs clearance.
Eager to speed up a cure, my "bright idea" was to cut a patch of 0.002" steel shim stock, sized to reflect the surface area of a 300 wsm brass. The shim was cut using a craft knife, rather than shears (to avoid any burred edges) and the finished piece rolled and slide in to the FL die.
After gingerly offering up a brass for sizing, I was delighted to find the shim stock instantly bedded itself inside the die and stayed safely in place whilst I re-sized 100 brasses.
Since the roll of shim had a butt joint, I opted to partially size, turn the brass, sized a little more, turned the brass again and finalize the sizing.
Whilst not planning to use these brasses for competition work, I am hoping they will at least give me a further 3 or 4 loadings for hunting or practise work.
... the proof will be in the eating and I will load up a few rounds tomorrow, check them for concenticity and also to see how they fire.
I am not suggesting my use of shim method is superior to using a custom made die, but at least it offers an instant remedy.