How's this for an idea?
One day you're bound to come across a trashed one. You could use this situation as "free" training, I've done it myself in the past, in different situations.
You could approach this by explaining to the customer that due to shrinkage risks it may not be possible to clean this carpet satisfactorily, because of the issue with high soil/low moisture requirement. Test the water a little, pose the question that if the carpet won't clean up to a satisfactory result would they probably just replace it? If the answer is a definite "yes", ask them if they would be willing for you to attempt cleaning it anyway, at no cost to them but with no guarantee of the outcome.
Emphasise that you can try a "last resort" approach that does carry a chance of shrinking the carpet, but reaffirm that if shrinkage does occur they won't be losing anything as they'd be replacing it anyway. You need to make sure they are in full understanding and agreement on this matter!
If they agree,
get them to sign a disclaimer and fire away at it with HWE! Get it a little wetter than you'd normally dare and see what happens.
I bet you'd find that as long as the fitting's sound you could quite a bit more moisture than you thought! You may even end up with a miracle result and a few quid for your trouble. You may also end up walking away from a smiley-edged carpet with nothing for your trouble apart from an important lesson learned