Are you saying that you have had similar conversations with other people?
Do yourself a favour. Make a list of all the possibilities you can think of.
Somewhere in that list there will be the scenario that the people who disagree with your idea about a sundial are distinct and separate AND that they disagree with you because there is something in your idea that CAN be disagreed with.
What you are doing is like using a nail to infer a hammer, then using both nail and hammer to infer a toolbox, when you already know the toolbox contains a nail and a hammer.
Without that proir knowledge the nail on it's own PROVES nothing.
You even said so yourself.
You would need to CHECK the accuracy of a sundial by using ANOTHER tool. What does this tell you?
It PROVES that a sundial cannot be trusted.
You are projecting future knowledge into a past where that knowledge didn't exist. There is nothing wrong with trying to find a simple illustation of a complex issue but a sundial is dead in the water when used as an illustratiion of time.
In another post I asked why the ancient greeks didn't have mechanical clocks when they had mechanical orrories.
Could it have been that they hadn't made the connection between the movement of the heavens and time?
Think about why that was.
Hint. Could it have been because observation suggested that the heavens moved at varying speeds (because of subjective time).
Think about that, you have an orrory. You know the orrory is mechanically accurate because you have designed and constructed it yourself. You use the orrory whilst watching the stars that it represents. It confirms that your engineering logic and skills have accurately depicted the movement of the stars. Subjective time still tells you that both orrory and stars speed up and slow down.
This tells you nothing that you didn't already know. It appears to CONFIRM an erroneous concept of time (again for a given value of erroneous).
Science isn't about proving yourself right. It is about trying to prove yourself wrong. A failed experiment tells you more than a successful one because it refines a concept. A successful experiment only confirms that the experiment has been correctly designed to produce the result that you expected.
Thus the greeks never twigged that the technology of an orrory could be used as the basis of an accurate timepiece.