We work for some contract cleaners doing their carpet cleaning, that works. Contactr them and tell them you can take the hassle of carpet cleaning away from them as some of them don't like doing it but do it becuase their clients ask. You can't win 'em all but some will.
We also make sure that when we tender for jobs direct we stress we're not contract cleaners who clean carpets, all we specialise in is carpet cleaning. Then point out all work done to the PAS standard etc with links to that in the tender document. Then suggest they check any other contractor is aware of and works to those standards. That has won us some contracts, just becuase the other cleaners haven't even heard of the standard.
We've also had examples where they let the contract cleaner take on the carpet cleaning, but they came back after the first year saying the standard wasn't as good, may have been cheaper but standard was not good.
Just make sure you leave the door open for them to come back, leave them some spotter product "just in case" and make sure they stay on your email newsletter.
Al.