Irving's Past Might Be Much Darker
The season 1 finale established that Irving served in the U.S. military. That much we know. This leads one to believe that Irving chose to sever in part because of lingering PTSD related to his service.
With this last episode, I believe that Irving severed moreso as a way to cope with extreme guilt.
Irving was the first, and up until the group trip, only member of MDR to suspect Helly. The odd detail about the "night gardener" is not something that most people would catch, let alone catch immediately.
He then acts surprised when Helly touches him in an act of comfort, looking down at her hand and then up at here with a slightly suspicious frown, since that's not something innie Helly would usually do.
The final detail that made him certain was when he asked Helly "Hey kid," and she didn't respond with their inside joke response of "What's for dinner?"
These are all subtle behavioral differences that are not easy for even a regularly trained soldier to pick up on. This indicates that Irving has specialized training which allows his subconcious to remember meticulous details and immediately pick up on even the smallest of character inconsistincies.
Leaving Helly aside for a bit, when Irving leaves the campfire and gets lost, ultimately tripping and dousing his torch, he doesn't panic. He doesn't keep shouting for help, he doesn't try to run back to where he thinks the camp might be. He finds a nice rock to rest his head and goes to aleep. How many times has Irving had to sleep outside in the wilderness before without a tent or even a source of heat or light, and for what reasons? Seems like something a special ops agent would be used to.
Back to Helly, what does Irving do when he's certain it's outie Helly? He Grabs her by the hair and starts drowning her in a river. His first instinct is torture. What's more is that doing this to Helly seems effortless. He's able to very easily keep her down despite resistance, and knows exactly how long to leave her head underwater before pulling her up for a breath.
He also refers to her as a "mole," which seems very purposefully chosen as that term in particular is highly associated with espionage.
For one last detail, if I were in Irving's place while drowning Helly, I would personally be freaked out by the fact that I just literally tortured someone after pulling her out. Irving is not only completely calm and collected at this fact, but he immediately switches to trying to comfort innie Helly. He's done this before. It doesn't phase him.
I believe that Irving was in some sort of counter-intelligence arm of the military that picked out certain high value targets, going so far as to then interrogate and torture them.
Irving did not sever because he was traumatized by war. He severed because of the extraordinarily horrible things he did in war. Maybe his outie's investigation into Lumon is some sort of self-inflicted pennance.
Or hell, if we want to REALLY get out there, maybe Irving never actually left the military. Maybe his investigation into Lumon is a part of a much wider operation... but I'm not too sure about that one.