Click /mute all, mute pings, and treat ranked as if it was solo player. This is what I did when I was 2 week banned back in season 4 before tribunal went down, it worked but a few years later my hard tilt rage reared its face and I'm 2 week banned again. So soon as I'm off I am just hit that /mute all and only call for drags and baron.
The key here, atleast for me, is to get your teammates to not rage at you, but to rage at other teammates. People will love to find sceapegoats and bait you into raging so they can report you. If you mute them they will realize you are not responding to them and thus think you have them muted, which you do. This will then have them turn on someone else to scapegoat and bait into raging instead, keeping all focus away from you. Not typing will also significantly improve your play and its how I got gold for the first time when I got off my first ban years ago.
This game would be so much better if there was a "disable chat" button like HoTS has.
Seriously tho, the new system is very sensitive to players coming off of 2 bans compared to before. If you say even ONE THING negative you are going to get permed, so muting chat is your only option if you can't control your raging.
if that doesn't work and you just rage for no reason every time someone makes a mistake, then I hate to say it but your account is done. Youre best bet is to make a smurf now and play on that and just not play on your main for like an entire season. You won't be on your main for 1 year, but atleast it won't get permed and will eventually be reset to good standings with the system.