-So there's a clear explanation in post #4 as to why it's not possible to run the waste out through the wall to the external waste pipe
-The water pipes are not hidden under the floor or in wall because I foolishly hired a professional, who turned out to be out of his depth, to install the bathroom
-Yes, you're absolutely right that I can run the bath waste under the floor and back up to the black waste
-No explanation, clear or otherwise, in post #26 of what more information might be useful to provide
So, bickering to oneside, what additional information would be useful?