If we remove ourselves from that position, maybe Israel will learn and be motivated to give a little (diplomatically) for their own security.

I don't think that would be the likely outcome. Israel probably regards the formation of a Palestinian state at the Green Line borders without an agreement on the Right of Return to be a much greater security risk to them than the withdrawal of U.S. support. That's where they were in the 1990's before the Second Intifada, and the events of the last twenty-five years have only made that opinion stronger, IMHO. I think they would calculate that while both options are bad, they're better off trying to move forward without the U.S. than doing what you suggest would be necessary to win our support back.

I guess the follow-up question is, would they be able to persist without U.S. support? Do they need the U.S. in order to maintain their security?