Praise be to Allah.
Firstly: What you have read about the virtues of reading Soorat al-Muzzammil is not correct, rather it is a fabricated hadeeth and it is not permissible to follow it or take it as evidence.
It was originally narrated from Zirr ibn Hubaysh from Ubayy ibn Ka’b (may Allaah be pleased with him) who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) recited the Qur’aan to me twice during the year in which he died, and said: “Jibreel (peace be upon him) told me to recite the Qur’aan to you, and he sends greetings of salaam to you.” Ubayy said: I said when the Messenger of Allaah (peace and blessings of Allaah be upon him) recited to me: “It is as if it was just for me; did you single me out for the reward of Qur’aan because of what Allaah told you?” He said: “Yes, O Ubayy. Any Muslim who recites the Opening of the Book (al-Faatihah) will be given as much reward as if he recited two-thirds of the Qur’aan, and he will be given reward as if he had given charity to every believer, man and woman… and whoever recites Soorat al-Muzzammil will be relieved of hardship in this world and in the Hereafter.”
Ibn al-Jawzi (may Allaah have mercy on him) said: And he mentioned a reward for every soorah until the end of the Qur’aan… this hadeeth about the virtues of the soorahs is undoubtedly fabricated. Al-Mawdoo’aat, 1/391.
Al-Shawkaani (may Allaah have mercy on him) said: This was narrated by al-‘Aqeeli from Ubayy ibn Ka’b in a marfoo’ report. Ibn al-Mubaarak said: I think that the Zanaadiqah fabricated it.
The hadeeth has several isnaads all of which are false and fabricated… and there is no dispute among the huffaaz that this hadeeth of Ubayy ibn Ka’b is fabricated. A number of mufassireen were deceived by it and mentioned it in their Tafseers such as al-Tha’labi, al-Waahidi and al-Zamakhshari. No wonder, because they were not versed in this area of knowledge.
Al-Fawaa’id al-Majmoo’ah fi Ahaadeeth al-Mawdoo’ah, p. 264
The fact that this hadeeth is false was mentioned by Ibn ‘Adiyy in al-Kaamil (7/2588) and by al-Suyooti in al-La’aali al-Masnoo’ah (1/227) and by al-Dhahabi in Tarteeb al-Mawdoo’aat, 60, and by others.
Note: Many ahaadeeth were fabricated about the virtues of various soorahs of the Qur’aan. Their fabricators’ intention was to encourage people to read Qur’aan and devote themselves to that, and they claimed that they were doing good thereby. But their intentions were misguided because that is undoubtedly subject to the stern warning contained in the words of the Prophet (peace and blessings of Allaah be upon him): “Whoever tells a lie about me deliberately, let him take his place in Hell.” Narrated by al-Bukhaari, 10; Muslim, 4. It makes no difference whether the lie is intended for good or for evil.
Mu’ammil ibn Ismaa’eel (d. 206 AH) investigated this hadeeth until he found the person who admitted to fabricating it. Mu’ammil said: A Shaykh told me this hadeeth and I said to him: Who narrated this to you? He said: A man in al-Madaa’in, who is still alive. So I traveled to go and see him, and I said: Who narrated this to you? He said: A Shaykh in Waasit. So I traveled to go and see him, and I said: Who narrated this to you? He said: A Shaykh in Basrah. So I traveled to go and see him, and I said: Who narrated this to you? He said: A Shaykh in ‘Abadan. So I traveled to go and see him, and he took me by the hand and led me into a house, where there were some Sufi people and a Shaykh with them, and he said: This is the Shaykh who narrated it to me. I said: O Shaykh, who narrated this to you? He said: No one narrated it to me; rather we saw that the people had turned away from the Qur’aan, so we fabricated this hadeeth for them, to turn their hearts back to the Qur’aan.
Another example is the hadeeth of ‘Ikrimah from Ibn ‘Abbaas (may Allaah be pleased with him) concerning the virtues of the Qur’aan soorah by soorah. Its fabricator, Nooh ibn Abi Maryam, was asked about it and he said: I saw that the people had turned away from the Qur’aan and were preoccupied with the fiqh of Abu Haneefah and the maghaazi of Muhammad ibn Ishaaq, so I fabricated these ahaadeeth for the sake of Allaah.
See al-Mawdoo’aat by Ibn al-Jawzi, 1/394; Sharh Muqaddimah Ibn al-Salaah by al-Iraaqi, 111.
With regard to Soorat al-Mulk, we have already discussed its virtues in question no 26240.
May Allaah help us all to do that which He loves and which pleases Him.