Both Jeremiah and Ezekiel prophesied that believers would have “a new heart” (Jer. 31:33, Ezek. 11:19-20 and 36:26-27), and Paul and other N.T. writers seem to indicate this prophecy has come true in Rom. 2:29, Rom. 6:17, and Heb. 8:10. Would you say that this prophecy has been fulfilled or do you believe the new heart is not yet available to us?
The promises of Ezekiel 11 and Ezekiel 36 were intended for Israel in the Millennium, and Jeremiah 31 is a promise that Israel will one day receive the New Covenant, so we’ll focus on the New Testament. None of the references you cited actually promise a new heart to believers, nor are there any that do. In fact the phrase “new heart” does not appear in the New Testament.
But I believe there’s been a partial fulfillment in that believers can recognize sin, feel the conviction of the Holy Spirit, and seek forgiveness, something non-believers can’t do. However I don’t believe our hearts will be made new until we’re perfected and divested of our sin nature. This will happen at the Rapture when we’re changed in the twinkling of an eye.