Either we have a complete contradiction between scriptures if your inference is correct or we have God demanding from man what only God can do, thus providing man with no other alternative to accomplish this command then reliance upon God?
I believe it is the latter not the former as you are inferring because:
1. Scriptures deny it is possible for man to remove his transgressions and thus impossible for man to cleanse his own heart and spirit from sin.
2. Scriptures deny it is possible for man to produce a new heart and spirit as that is a creative act that only God can do.
Hence, this command falls into the same category as "do this and live" in regard to the Mosaic Law or "be ye therefore perfect even as Your Father in heaven is perfect." Neither is possible for any man to do which drives man away from himself, his own power, his own works to acheive these ends. That is the point of giving the law to reveal inability to do these things and direct them toward God through Christ to accomplish all of these things.
Calvinist do not see any conflict with these statements as the natural state of the fallen depraved nature is to harden the heart to whatever light in whatever area of their life they are being exposed to light (Rom. 8:7-8; Jn. 3:19-20).
This an individual commandment. This does not prove or disprove Calvinism as among the children of Israel there were saved persons in whom the Lord created a new heart and spirit (Moses, Caleb, Joshua, Aaron, Miriam, etc.) while others would not be willing.
This has nothing to do with personal salvation but with the direction which God had told them to travel. There could be mulitude of reasons why they would or would not obey this which would have nothing to do with defining individual salvaiton status.
You need to read the context better. He is saying IN CONTEXT that they in rebellion against God and are acting soverignly, thus replacing the heart of God with their own heart as though they are God.
This is man's duty but it does not say anything about his ability to perform this duty. This falls in the same category as removing their transgressions from their hearts and spirit, and "do this and live" and "be ye therefore perfect even as your Father in heaven is perfect." None of these commandments are possible for fallen man or regenerated man as they are creative acts of God and or conditions of sinlessness that fallen man has already violated.
paul in Romans seemed to think that fallen/natural man is IMPOSSIBLE state/condition to either come to God, or else keep the Law, as while law was/is perfect, sinful flesh cannot keep it....
God HAS to be the agent granting new hearts, and new condition/state between us and Him, for we can do NOTHING in sinful/weak flesh!