I may be out of my depth here, but I must sat I disagree with the vast majority on this issue of "fully ready" and indeed slightly on the issue of being ready on reaching. I'm not disputing the instructions for proper RT, merely the argument about the use of English.
ZOOKER, rightly said in my opinion that context is key to a ready message. Is the "ready on reaching" not that context? As a paraphrase of "ready to depart, on reaching HP" ? Perhaps I am wrong.
Most importantly though, readiness is not a bi-polar state I believe. It is possible to be in a partial state of readiness. This could be why the military use a scale for readiness for example. Allow me to submit an example.
(As with many terrible stories, I have chosen to set the scene with a camping expedition - A gory end to many a fictional hero!)
You are out camping, and your friend says "we have to go in 5 minutes". You know it will take you 10 minutes to pack your things away.
However, after 8 minutes, a group of axe murderers runs towards you in a murderous rage. I believe, that whilst you are 2 minutes from being "fully ready" you will find yourselves very much ready enough to take some departing action, without any delay at all!
An unlikely story, to be sure. But the point stands I hope.
Phil