Let me spell it out. You ask, "Have you had an expriance of non-finite regression of thoughts?". By its nature, something which is infinite is not going to end. If someone was able to tell you they had experienced such a thing, then it wasn't infinite. Perhaps you could explain clearly what you meant instead.
Let me help you to be aware of your inconsistency about the non-finite.
By your "up to" you had no problem to say that the non-finite is stopped at some finite value, called Limit (or any other name that you like, it does not matter).
Jsfisher and his community are using (and teaching all around the world by academic institutions) exactly this bogus argument in order to solve the A\T Race (infinitely many values, where each one of them is not 0, are summed to some accurate value by a finite amount of time).
Poor Cantor was afraid of the non-finite, so he invented the transfinite cage in order to control the cause of his fears.
The first cage is called Aleph0, which is a fixed value that no natural number can be escape from it, because Aleph0 is bigger than any natural number that is caged by it.
Then Cantor discovered that Aleph0 cage is too small for irrational numbers, so we need a bigger cage, called Aleph1.
But then Cantor discovered that any power set of a given set needs a greater cage than the set, etc …
So Cantor discovered that the very idea of caging the non-finite, is impossible.
Instead of investigate this simple fact (the non-finite is not cage-able) in order to really understand it (which terrified him) Cantor invented the CH problem, which is a kind of a cage that is made by Aleph0 and Aleph1 as its borders.
Gödel, in principle, made the same mistake. He discovered that formal systems that are powerful enough for Arithmetic are incomplete, because there are always truths in those systems that cannot be proven within them (Conclusion: formal systems are generally incomplete, and we can say bye bye to Hilbert's mechanic program).
Instead of investigate this simple fact (the non-finite is not cage-able) in order to really understand it Gödel tried to capture it by the same tools (verbal-based symbolic Logics) that actually "told" him: "We are incomplete by nature".
Both Cantor and Gödel actually discovered the fact that no collection of lower dimension, magnitude, etc … (the name is not important) can be a higher dimension, magnitude, etc … , and one of the simplest examples is based on the fact that no collection of points can be a line, or in general: "Non-locality is not a collection of Localities".
What the "lovely" community of jsfisher made is this:
Instead of get the simple notion of the non-finite as exactly what it is: NONE-FINITE, they continued to swap off this natural fact under a new invention called Proper Classes, and then they are inventing the Power of Proper Classes (and give it some fancy name) etc... atc... and they will do any possible maneuver in order to avoid the fact that the non-finite is a non-cage-able beautiful beast.
Do not bye a cage-able non-finite beast in the market, because it is a bogus one (unless you are afraid of the real thing).