I think this is just the result of the pattern that makes up all of our diatonic scales/modes. Since they all have the same set of intervals, just rearranged, patterns from one should appear elsewhere. In this case, I'd say you're somewhat arbitrarily rearranging intervals and finding that pattern in a different way than you usually would.
Since there are 7 notes in a diatonic scale and a defined set of intervals, the possibilities of what you can get when reversing the order are very limited. It might be easier to see this if you write out the intervals forward and backward over more than an octave.
That's the major scale intervals forward and backward. Below, I have placed some brackets to show the pattern.
Notice how the major scale is still in the reverse section, just displaced. This shows that when you reverse the order of the intervals, you will find the same scale in there somewhere. Since all of the modes are made up of these same intervals, it follows that no matter which mode you start with, you will end up finding another one when you reverse the order.
I'd also say that this shouldn't really point to some broader connection beyond it being a pattern. When I say that you're rearranging things somewhat arbitrarily, I intend to say that taking the intervals and going in reverse isn't really something that we associate with being a different key or tonality, eg, it's still the major scale when you play it going back down the octave.
Having said all of that, I'm hopeful that this isn't discouraging. Finding this pattern may not have been relevant in the sense that you were thinking but in finding it, you've come to better understand some aspects of theory, at the very least, making you look deeper into the modes. This curiosity is key in finding enjoyment in theory, which many are not able. I personally have had a whole lot of experiences like this, thinking I had stumbled onto something remarkable and realizing it's not as great as I thought, and not getting upset over that has allowed me to continue pursuing theory as a passion. Deep analysis of things that others gloss over as simple constructs, like Modes in the general sense, is what can bring you to the next place that may actually be a true revelation for you, if not everyone.