First of all the hadith in Sahih Muslim has two parts:
I heard Allah's Messenger (ﷺ) as saying: When any one of you stays at a place, he should say:" I seek refuge in the Perfect Word of Allah from the evil of that He created." Nothing would then do him any harm until he moves from that place.
which was reported on the authority of Khawla bint Hakim as-Sulamiyyah and was also compiled in al-Muwatta'.
This statement already should clarify that saying this du'a is not limited to a timing.
Abu Huraira reported that a person came to Allah's Messenger (ﷺ) and said:" Allah's Messenger, I was stung by a scorpion during the night. Thereupon he said: Had you recited these words in the evening:" I seek refuge in the Perfect Word of Allah from the evil of what He created," it would not have done any harm to you.
Therefore one could say these words at any time of the day at least once (this was compiled by abu Dawod, at-Tirmidhi and ibn Majah beside a lengthy and somewhat strange version in Musnad Ahmad and in other sources which was discussed in the fatwa on islamweb #395182). The hadith doesn't set a limit for repetitions.
Note that the hadith of Muslim above is the second version of the hadith (so it is a backup evidence of the Sahih hadith). If al-Bukhari and Muslim repeat a hadith in the same chapter the first quote is that of higher quality and confidence and the more you go on the less quality is in either the chain or content, but still their conditions of sahih are met).
Therefore it doesn't seem to me much beneficial to check all sources of the hadith and their validity or quality.
Saying them trice in the evening has further a strong evidence (which was reported by at-Tirmdihi in his Jami') .
Abu Ya'ala al-Mosily confirmed it for the evening without quoting an amount in report with a sahih sanad and add that it can be said in the morning and evening in a marfo' narration based on an-Narration with the same chain with an addition of rafa' which was reported via 'Ubayd Allah.
The fatwa mentioned above says there's no harm to recite this du'a in the evening or morning. It further said that it was also mentioned in the book of ibn as-Sunni, that of ibn abi Shaybah and al-Haythami in Ghayat al-Maqsid.
Only at-Tabarani (so far my search results) compiled a version mentioning morning and evening
This verison is on the authority of abu Hurairah and mentioned in his al-Awsat:
523 - حدثنا أحمد بن القاسم قال: نا محمد بن إبراهيم، أخو أبي معمر قال: نا إبراهيم بن أبي بكر بن المنكدر، عن سهيل، عن أبيه، عن أبي هريرة قال: قال رسول الله صلى الله عليه وسلم: «من قال حين يصبح وحين يمسي: أعوذ بكلمات الله التامات من شر ما خلق، لم يضره شيء»
At-Tabarani also mentioned several other versions and commented on that of the tree times as reported by at-Tirmidhi, which he compiled based on similar chain of transmission #6038 saying:
لم يرو هذا الحديث عن حماد بن زيد مجودا، عن أبى هريرة إلا محمد بن سليمان " ورواه الناس عن حماد، عن سهيل، عن أبيه، عن رجل من أصحاب النبي صلى الله عليه وسلم
None except Muhammad ibn Sulayman reported this hadith via Hammad ibn Zayd in a correct (good? free from mistakes?) manner. But people reported it from Hammad from Suhayl from his father from a man from among the Sahabah
At-Tirmidhi reported it via Yahya ibn Musa, from Yazid ibn Haroon, from Hisham ibn Hassaan, from Suhayl from his father from abu Hurairah.
While at-Tabarani reported it via:
Ahmad ibn al-Qassim أحمد بن القاسم (trustworthy),
from Muhammad ibn Ibraheem the brother of abu Ma'amar محمد بن إبراهيم، أخو أبي معمر (Sadooq),
from Ibraheem ibn abu Bakr ibn al-Munkadir إبراهيم بن أبي بكر بن المنكدر (acceptable, ad-Daraqotni regarded him as da'if),
from Suhail ibn Dhakwaan سهيل (trustworthy, had some mistakes),
his father Dhakwaawn ذكوان also known as abu Salih as-Samman (trustworthy) -> abu Hurairah.
