Man I used to be in a similar boat. Actually, to be honest, this is the first season i've really played ranked. Most other seasons I play 20-30 games total and never really tried to climb because I found myself inherently getting frustrated.
"Oh my teams feeding"
"Everyone's fighting in chat"
"They aren't teamfighting with me"
"This dude is so TOXIC"
"Jungler is camping me"
"Dude is so negative/SPAMMING surrender votes"
But it occured to me as I was playing normal games; I literally treat the two identical- I PLAY TO WIN. So why is it I care so little if I lose a normal, but care so much if I lose a ranked?
So I tried something different, kinda like the last sentence you implied. I stopped caring about winning. Yes, I still try effectively the exact same amount, but I do not care if I lose. In fact, two or three of my wins that have got me to G3 now are from games where someone literally spammed the ff vote at the earliest time he could re put it up. "Mid sucks" , "Mid fed my lane" "Lol gg surrender" "gg", constantly. I just muted him and kept playing and saying shit like "Ok I think we can get back in this one guys". Before I knew it, we were winning teamfights with an inhibitor down. Twitch stopped spamming surrender votes. In fact his support was saying - that now he was saying "ok I can carry this (lol)". We ended up winning it despite it being one of the most obnoxious players i've ever played with (and he genuinely believed he carried the game, although we certainly wouldnt have won without him either).
In any case, I know its not easy, but try not to care. When you care about the climb too much, you care too much about each individual game WAAAAAAY to much. From my own experience, i've taken a mentality of "Man, it would be nice to be Gold, but the fact of the matter is i'll end where i'll end", meaning even if I lose a bunch, thats where I deserve to be, because there are other players that HAVE had that and COULD carry it, means I just wasn't good enough. Good luck friend.