No, validity has to do with the logical structure of an argument or syllogism. You are using it in the colloquial sense. That's normally fine, but in a philosophical discussion is a bit confusing.
Evidence is not subjective if it is relevant and factual. You have had every opportunity to provide evidence and still you don't--I think you have none and are aware of it.
Define relevant and factual - especially in this post-truth world. You are over-intellectualizing everything you have encountered when it is blatantly clear that you want to hear what you want to hear. That is fine, but just don't pretend you are on a noble pursuit of absolute truth: you want to be vindicated in part and told something you will believe in general.
As I told you it is not the job of a Christian or layperson to convince another
adult of something: everyone is responsible for their own spiritual trajectory.
You are free to interpolate what you believe I am saying; it won't get you closer to an acceptable apology. You have been given the answer to your questions several times, but your own mind prevents you from realizing you already have what you need. You are fighting the air. Remember, you are the one who is asking the question:
My longer form question is: given all the above, should Christians engage non-believers on this forum by engaging in apologetics and by attempting to make compelling arguments for their claims as a way to convince them those claims are true?
And your own behaviour should be a huge sign
to you the answer to your question: apologetics are futility. Maybe if you make a list of all the evidence acceptable to you, the boundaries of what you believe and accept and how you view the world around you someone will be able to make an argument. But, for example, you didn't even believe the election was true
when you were a Christian - despite the dozens of verses that explicitly detail both the election and predestination by
prophets, the disciples and Christ. So, you have a long way to go before you transform your (completely unnecessary) hyper-intellectualism into an open mind capable of understanding spiritual things. If you ignore the meat for syntax (or if you don't realize a word, for example, is
rooted as a verb *ahem*) then you handicap your own progression, and prevent yourself from gaining kernels of truth. Atheism and agnosticism should be a
step in enlightenment; staying at this step just enhances the salt and vinegar chip on your shoulder.
But good luck to you; remember what was said about the fool and learned person arguing...