I'm in pretty much the same boat re: calculus, but I think a lot of it has to do with problems just like this. For me, early in my experience with calculus I always looked for the "graph it out"/non-calculus solution. So problems like water leaking out of a bucket, rocket acceleration, and other integrals where the underlying process is in some way linear always fell to non-calculus-based analysis. And thus when I got to problems where actual calculus was required, my non-grounding in the basics pushed me toward rote memorization which (of course) didn't stick over years of non-utilization.