Same problem with ki. Extending ki through a limb is one thing--extending ki beyond the limb is quite another. Yet the sensation of extending beyond the limb vs. not is quite different--both for nage and uke. This makes sense if you view ki as a flow through a channel--less so if you consider it to be primarily about organizing the body.
"Extending ki beyond the limb" sounds perilously close to ki ball demonstrations and knocking people off their feet from 10 feet away, although I'm sure you are referring to something else entirely. For example, there are times that when I uke for Mary I'll say to myself "this is a really bad idea" before we ever make contact. I will feel something in me, not a force acting at a distance, but a feeling of unease and my impression of her will be one of a person taller and more imposing than she is normally. What I am experiencing in that moment is an extension of her ki, which is the result of her coordinating mind and body to a very high degree. I used to have the same feeling whenever I was uke for Maruyama sensei.
I don't view ki as a flow through a channel. I see it as a result of mind and body being tightly coordinated and highly focused. It's more than body organization, it's about the organization of mind and
body. And once ki is manifest it can be manipulated via intent, to the extent that it can be felt across a distance by uke.