This hadith supports your view. But it's one hadith, and agreed upon beliefs (Aqeeda) can't be formed on khaber wahed (sole narration).
I already showed a ziyarat of Imam Ali (a) being called the Messenger of God. There is also this Du'a of Imam Zainal Abideen (a):
اَللّٰهُمَّ يَامَن
O Allah, O He who
خَصَّ مُحَمَّدًا وَآلَهٗ بِالْكَرَامَةِ
singled out Muhammad and his Household for honour,
وَ حَبَاهُمْ بِالرِّسَالَةِ
loved for them the messengerhood,
وَ خَصَّصْهُمْ بِالْوَسِيْلَةِ
specified them for the mediation,[347] so
وَ جَعَلَهُمْ وَرَثَةَ الْاَنْبِيَآءِ
appointed them the heirs to the prophets,
وَ خَتَمَ بِهِمُ الْاَوْصِيَآءَ وَ الْاَئِمَّةَ
sealed with them the executors and the Imams,
وَ عَلَّمَهُمْ عِلْمَ مَا كَانَ وَ عِلْمَ مَا بَقِيَ
taught them the knowledge of what has been and what remains to be,
وَ جَعَلَ أَفْئِدَةً مِنَ النَّاسِ تَهْوِي اِلَيْهِمْ
and made the hearts of the people incline toward them!
فَصَلِّ عَلٰى مُحَمَّدٍ وَآلِهِ الطَّاهِرِيْنَ
Bless Muhammad and his Household, the pure,
وَ افْعَلْ بِنَا مَا اَنْتَ أَهْلُهٗ فِي الدِّيْنِ وَ الدُّنْيَا وَ الْآخِرَةِ
and act toward us with that of which Thou art worthy in religion, in this world, and in the next world!
اِنَّكَ عَلٰى كُلِّ شَيْءٍ قَدِيْرٌ.
Thou art powerful over everything.[348]
وَ كَانَ مِنْ دُعَآئِهٖ في الصلاة على آدم
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This also reminds of a verse that people associated with Ahlulbayt (a) a lot in the hadiths:
4 - حدثنا أحمد بن علي بن إبراهيم (رضي الله عنه)، قال: حدثنا أبي، عن أبيه إبراهيم بن هاشم، عن علي بن معبد، عن واصل، عن عبد الله بن سنان، عن أبيه، قال: حضرت أبا جعفر محمد بن علي الباقر (عليهما السلام)، ودخل عليه رجل من الخوارج، فقال: يا أبا جعفر، أي شئ تعبد؟ قال: الله. قال: رأيته؟ قال: لم تره العيون بمشاهدة العيان، ورأته القلوب بحقائق الايمان، لا يعرف بالقياس، ولا يشبه بالناس، موصوف بالآيات، معروف بالعلامات، لا يجور في حكمه، ذلك الله لا إله إلا هو. قال: فخرج الرجل وهو يقول: الله أعلم حيث يجعل رسالته (3).
Ahmad b. `Ali b. Ibrahim (ra) narrated to us. He said: My father narrated to us from his father Ibrahim b. Hashim from `Ali b. Mu`abbad from Wasil from `Abdullah b. Sinan from his father. He said: I was with Aba Ja`far Muhammad b. `Ali al-Baqir (as) when a man visited him from the Khawarij. So, he said: O Aba Ja`far! What do you worship? He said: Allah. He said: Did you see Him? He said: The vision of eyes cannot comprehend Him. Rather, it is the hearts that will see Him through the realities of faith. He is not known by analogies, nor is He comprehended by the senses, nor can He be compared to the people. He is described by His signs and He is known by His indicators. He does not oppress in His wisdom – surely, this is Allah, there is no deity except Him. So the man left while saying, “
Allah is most knowing of where He places His message” (6:124).
Al-Amālī, The Forty-Seventh Assembly, Friday, the Fifth of the Month of Rabi` al-Awwal, 368 AH., Hadith #4
The Forty-Seventh Assembly, Friday, the Fifth of the Month of Rabi` al-Awwal, 368 AH.
thaqalayn.net
There is also Ziyarat Jamia Al-Kabir, where they are said to be "the place of the messengerhood/message" (madinal Resalah).
In verse 6:124 we can see the definition of Rasool is clear, it's where God places his message. There is similarly wording and it pertains to the contention of people of the Messengers.
We can say there is a contradiction in this regard in hadiths. So we have to turn else where then hadiths since there is a contradiction in the hadiths.
As for your definition, it's problematic clearly with Lut (a) for example stated to be a Messenger in Surah Poets "I am towards you a trustworthy Messenger". Lut (a) is a nephew of Ibrahim (a) and Quran says "so believed in him (Ibrahim) Lut (did)". And so Lut (a) would be akin to Ali (a) and Haroun (a) as far helper type and contemporary type. Haroun (a) is also stated to be a Messenger into two verses.
Also as far I'm aware, Musa (a) never emphasizes to Pharaoh nor Lut (a) to his people, that they are NABIS even though they are. This is because Nubuwa is purely about scripture and them being a channel. In case of Musa (a), he received scripture AFTER Pharaoh was destroyed while Quran says that Musa (a) was sent to Pharaoh as a Messenger. So this means messenger does not need scripture. It's the message, and it doesn't have to be direct words from God, as Musa (a) conveyed and paraphrased what he understood of God's message in his words. He wasn't channeling scripture at this point.
There are also many verses showing all that is upon the Messenger is the clear conveyance and we see in Surah Yaseen, three sent ones upon them is the clear conveyance, hence all three were Messengers.
There is also a line from Imam Ali (a) in Nahjul balagha,
أَمْ أَنْزَلَ اللهُ سُبْحَانَهُ دِيناً تَامّاً فَقَصَّرَ الرَّسُولُ (صلى الله عليه وآله) عَنْ تَبْلِيغِهِ وَأَدَائِهِ؟
This shows there's a difference from what God revealed of the religion and the Messenger (Mohammad) conveying it. This shows God revealed the religion, but the Messengerhood is about making sure a clear conveyance of it occurs.
And this is verified also in 5:67 which the message would be incomplete if Mohammad (s) didn't convey regarding Ali (a) at Ghadeer.
5:67 shows the messages of God aren't necessarily scripture. Actually, you never find a verse saying "upon the Nabi is only the conveyance", because the Nabi job is to channel scripture and establish it as a legacy and proof, while the job of a Messenger is to convey clear understanding. Since the Nabi job is more of God's role you never find "it's upon the Nabi only".
So on this definition, Nabis who are not Messengers and Imams who are not messengers, would be only if clear conveyance of the messages are established and do not need to be revived and established.
If there are disputes, then a Messenger is needed to be referred to, because the understanding is off and there is confusing or sleep of people regarding the reminders.
