In terms of my preferences, I tend to like a balance between story and dice-rolling, and write 1-2 page backstories for my characters. I also like a cinematic style where failure means a temporary setback - however dire the situation looks, in the back of our minds we expect the heroes to succeed most of the time and achieve their objectives, and characters die only in dramatically satisfying ways if at all.
When I'm running a game, I can make that happen and people are usually OK with it. However, I also like playing. I live in a rural area so my steadiest opportunity to do so over the years is a group of friends from college, now long-distance. The GM likes a grittier, more dangerous style, where rules are rules and dice are dice and he won't save you if you do something stupid, and also the challenges are set slightly higher so there's a risk of real failure.
Now, let me be clear: I'm aware of the Same Page Tool, we've talked about it, and nowadays I generally don't play when they're doing Dark Heresy or similarly grim games. This time we're doing a 'standard' DND5e campaign, at what I perceive as a pretty average level of challenge, where the GM is setting us up against tough foes but trying to avoid TPK. I've accepted the game under these conditions and I am having fun, but I've realized that I would be having more fun if I took my character's setbacks a little less personally and adopted an attitude of "seeing how the story goes, one way or another" rather than trying to "win" all the time. (I'm not that competitive normally so this is kind of out of character.)
For example, recently we had a tough fight at the conclusion of a storyline, and the toughest foe got an humorously unreasonable number of crits. Three of us were down, the last had 5 HP, and we had a few death saving throw failures between us before we got some last-minute NPC help. So things worked out and it was a fun session, but I realized afterwards that if we hadn't had the crits to joke about and the fight had gone that poorly due to normal-high enemy rolls, I wouldn't necessarily have enjoyed it overall. If I were a neutral observer, though, I would have said it was a dramatic nail-biter but not a problem, just an interesting turn of events.
So, my question: Having made the decision to do so, how can I adjust my thinking to accommodate this more-challenging style? Especially hoping for personal experience of "How I Learned to Stop Worrying and Love the RNG", but more general advice is also OK. Note that I'm not only concerned with character death, but with smaller ups and downs where my character would reasonably get frustrated, but I as a player shouldn't.
(Note: I grew up playing GURPS where character creation is a big deal, and that's what I usually run. I've played Dark Heresy and really didn't like the system (40% chance of success is considered high, and permanently losing a Fate point to avoid death means a major tool for survivability goes down over time instead of up). I've also run Risus and played 3.5 and Star Wars Saga Edition, plus a little bit of: Hackmaster, Pathfinder, KAMB!, Call of Cthulhu, Serenity, and Microscope. I didn't really have this problem with KAMB! since it's a one-shot and the object of the game is more about seeing your characters fail hilariously than trying to accomplish anything, and I imagine Paranoia might be similar, but I'm not sure how that helps in DND where you expect to play for at least a couple months.)