You're asking, in part, for a new term that can be used to attack people. I think that's the logical error here. It matters a little what the term is, but only a little. You could say that people have "gwizzy", and if they think it's being unfairly used to attack them, they'll hate the use of the term and will stop listening when you say it.

(Example: the word "retarded" used to be simply a neutral description...but people love to put others down, and so the word acquired a strong negative connotation. Switching to "special needs" helped a little bit for a little while, but now "special" has a negative connotation and that's growing. Newspeak doesn't work.)

If you go back to the message of love, how is it loving to insinuate that people are being treated too fairly, are being treated too much based on who they are as opposed to what stereotype you might paint them with? The words aren't the main problem. It's the sentiment associated with the words.

At this point, you're correct that you probably can't say "white privilege" and get any traction in a debate. You may as well call them a doody-pants. So, granted, if you actually want to sway people in debate, the term has got to go. (However, the more hated it becomes by the "other side", the better it becomes as a rallying call for people who agree with you.)

As others have said, the solution is to change focus. Rather than focusing on what some people have, you should focus on what others don't have but ought to have. People are much happier to support others gaining rights than to support the insinuation (even if you don't really mean to make it) that they should lose some of their own.

This also makes it much more relatable to white people who haven't really absorbed the point yet. "Can you imagine if you go apply for jobs and half the applications get thrown out just because of how they imagine you when they read your name? How is that fair?" You can start where they are and draw the contrast. In contrast, if you start with the idea of "white privilege", you're not starting with them. You're starting with someone else, and drawing the contrast as an apparent attack on them...no wonder it doesn't work! (If you're not talking to them, no reason to start with them, of course.)