I submit that conceptualizing 3.9999... is a more direct experience
I don't really see how you can assert that. Let's get rid of the 3 - it's an irrelevance, and just have 0.99999... I do understand that the number of 9s can be continued for as long as one pleases, and that the number thus expressed would approach 1 as closely as one pleases. But 0.9999... will always be an irrational number, and 1 will always be a rational number. The difference is fundamental, as Cantor observed.
I can imagine 1 perfectly easily, but imagining a quantity less than 1 but approaching it to an arbitrary degree of closeness is not something I can easily conjure up in my mind's eye.