Here’s a Merriam Webster definition of mystical: “involving or having the nature of an individual’s direct subjective communion with God or ultimate reality.” Let’s start with that.
Does the Bible describe direct subjective communion with God? Yes, and this is not remotely controversial. Abraham met God and talked with Him. Moses conversed with God as a man speaks to his friend. Gideon argued with God; Jacob physically fought Him. Isaiah saw a vision that nobody else saw; God told John to look for the Spirit descending like a dove; Saul of Tarsus heard a voice where everyone else heard thunder.
What about today? Today, the Christian faith teaches that you can be a partaker in the divine nature. The Christian faith teaches that if you belong to Jesus, you have been born again spiritually, and are presently indwelt by God Himself in the Person of the Holy Spirit. The Christian faith teaches that the indwelling Spirit comforts and teaches you (among other things). If these subjective experiences are actually happening in your life, then you have a direct, relational experience of God Himself.
You might not like the word mystical to describe it, but…re-read that definition. If you have a real relationship with God, there it is.
If those things are not happening in your life…well, then you’re not a practicing Christian. I’m not saying you’re not going to heaven; how would I know? You and Jesus can work that one out. But if you do not have an actual, real-life experience of the realities the New Testament promises to God’s people, if those things aren’t actually happening in your life, then you do not have a Christian spirituality.
At best, you’re an ideologue whose drug of choice happens to be theology. Maybe your doctrinal paperwork is all in order, and that’s great as far as it goes. As far as doctrinal paperwork goes, Jesus was a Pharisee (and so was Paul) so you see how far that gets you.
Gentle Reader, I am confident of better things where you’re concerned — there’s lots of folks whose doctrinal paperwork ain’t caught up to what they actually do in real life. But that’s a problem, because that gap between your actual walk with God and the things you’re willing to affirm causes you to criticize people who are willing, not just to live, but to tell the truth. You need to update what you’re willing to say, so that it matches what you know in practice.
If you don’t, then you will push people into the arms of the enemy. When kids that grew up in the church go looking for a functioning spirituality at the coven down the street because all they ever saw at church was talk and moralizing, that’s on us. And it’s high time we quit talking like we don’t have the real thing, because we actually do.
Full Contact Christianity 
I’m not sure you went far enough here. The examples you cited of individual “subjective communion with God” were all predicated on a collective failure of the community of the people of God in that dispensation to hear and obey. I would argue that God has always wanted to commune directly with his people as a community. This was evident, if we have eyes to see, among Jacob’s household in the Joseph narrative (Gen 37-50), among Israel at Sinai (Ex 19), and among the nascent church throughout the book of Acts as the Spirit transparently aimed to communicate to/through the existing local body of believers. I would argue that even the Macedonian call was predicated on a collective failure of the community to keep propagating the centrifugal mission of Acts 1:8. By the time we get to the First Corinthians, Paul’s “call to communion” among a quintessential carnal community, I would argue that what seems prima facie to be a description of subjective communion between God’s Spirit and the individual human spirit in 2:6-16, is actually consummated only when the Spirit is given full rein to orchestrate “communal God-speech” among a collective gathering of spiritually receptive “prophets” (14:22-40).
So we have to ask, is the “prophetic awakening” prophesied by Joel at the end of the present age also predicated on a collective failure among the present people of God to commune with Him?
I agree that God repeatedly sought to commune with the people of God as a community, and that 1 Cor 12-14 establishes that same goal as the norm for a church community today.
Of course the collective failures you’re talking about in my examples are there, but “predicated upon” asserts a relationship I’m not sure I see. Practically speaking, I’m also not sure how important that is. Even if (in the big picture) the people of God are going to fail, that doesn’t mean the people in front of me right now are going to fail; my job is to shepherd the ones I can reach.
Perhaps I wasn’t as clear as I could have been. To your point, I think the forecast of collective failure is important precisely because some (like yourself) are called (much like the individuals you cited) to speak prophetically into the lives of those who have ears to hear. Thanks for helping fine tune our message.