According to your question, the 9th quality must be the constant chant of hare Krishna mantra..right? Its covered in 4th point .
When you say "is chanting hare krishna necessary for reaching the heaven" you violate basic essense of the gita.
As , rather than performing positive karma and tapas you will to eat the fruit of your karma, reach heaven or the higher dimensions or Loka.
So my point is, forget heaven!
The hare krishna mantra is the revolution which was started by Sril? Prabhupad as to awaken the consciousness towards lord krishna among all ingnorant masses . So , for a Lord Krishna devotee it is necessary to be "Krishna conscious" rather than confining his bhakti to a mantra and that to just for reaching heaven.
You can chant even "Aum namo bhagvate Vaasudevaya" or " Shri krushna govinda, hare murari , he natg narayan vaasudev" which were the mantras pronounced by great seers like Veda Vyasa. But the basic expectation behind it must be pure intention and love for humanity (the divinity in disguise).
I would end my note by saying:
Karma in material world without expectation of fruit (heaven) with constant remembrance of lord(chanting mantras) is the correct priority of mortals like us, as explained by lord Krishna in the Bhagvad Gita.