Oh god I have this exact problem too and it's such a frustrating inner battle. I also dodge the stress by playing mostly open and only doing series if I feel like I'm in a good groove (or when the rank up battle forces me) but I know I need to get over it at some point.
I try to counter it by telling myself it's not that big of a deal. I keep trying to convince my emotional brain with the practical stuff, like that any points lost can always be gained back, my actual skill matters more than my in-game rank, when my skill improves my rank will follow naturally anyway, so I just need to play the best I can, ignore the points, and trust that the system will do its best to put me where I need to be to keep improving (even though it doesn't always succeed, lol).
But honestly I haven't been having much success; the emotional brain doesn't listen to reason. So I try to reframe my losses in a narrative sense, like telling myself to imagine how much greater it will be when I finally break through because I struggled this much to get there, that persistence is the most important skill in improving at anything and this is just an opportunity to use and strengthen that skill, etc. Sometimes that works, but it's still quite a struggle.
So recently I have been attempting just a raw psychological approach via exposure therapy. Just forcing myself to play them regardless of how I feel-- not for the sake of progression and winning but just for the sake of getting more comfortable doing it. I've tried a few patterns but the one I'm on right now is that for every two open games that I win, I make myself go do a series game. Just one, then I can go back to open. Eventually maybe I'll up that to one series game for every open win, and then go from there. I've only just started doing it this season so I don't know if it's helping but it feels like it is, so we'll see I guess. The fact that I only do one series game and than go immediately back to open makes it feel less intimidating, and prevents me from getting too downtrodden about it if it's a loss because I just jump into another, much lower-stakes game before I give myself time to think about it.
And as a sidenote, (this is anecdotal but seems to be my experience) I feel like skill-matchmaking has been historically much better in series for me. So many of my open games have players with S+/X-rank badges (I've floundered between B+ and A the last few seasons) and they just kind of play out the game for me. I sometimes don't really feel like I'm getting a real experience of playing with people on my level, I'm just getting dropped onto/against teams of players more skilled than me and trying to contribute the best I can while barely making an impact. Not that that never happens in series but it feels less often. So I can sometimes leverage that to convince my brain to do series by telling myself that it's probably better for my development, which seems to have more persuasive power than anything else I've tried so far, hah.
I hope you can find something that works for you (and also if you do please let me know, lol)