I want to brainstorm with everyone on what can be done to combat this in way that cannot be abused, so people that are genuinely having a bad game aren't punished.
Responding out of order, but thank you for accepting this. Innocent players should not be punished, and the system should not lead to an increase in abuse. That's the most important things.
I think that perhaps there needs to be more moderation when it comes to reports in ranked games. Users who intentionally grief in ranked games should be issued penalties more frequently
So... there is a lot of moderation. Many intentional feeding reports (the ones the system cannot determine) are sent to manual review, especially those with comments of behavior. But, as you say, they do not want to risk people who are genuinely having a bad game be punished. If you "lower the bar" from what it is now (beyond reasonable doubt) to something like say, preponderance of the evidence, you will increase the amount of people punished incorrectly for intentionally feeding.
and then after so many penalties, they should be banned from ranked for the season.
If someone gets a second penalty for intentionally feeding, that punishment is a permanent ban. A ranked ban is unnecessary given that they aren't playing on that account anymore. Furthermore, Riot has stated in the past that they will not implement a "prisoner's island" of any sort - including using "ranked bans", multiple queues for "toxic" players, etc.
I was also thinking about a system that allows players to appeal a loss so that they don't lose LP when someone else is inting.
LP works because it works like a currency. Sure there are very rare instances where one team may win LP without the other losing any (loss prevented), but those are extremely rare. When you start to alter the "transfer" of LP from the losing team to the winning team, you end up artificially inflating/deflating the LP of the game. To fix this, you'd either need to shove all the LP loss onto one player (which would be over 100 LP in some instances, and would be way too severe a punishment in addition to the 2 week ban), or you need to reduce/eliminate the LP win of the other team (unfair to them).
However, I figured that could be too much as I could see people unnecessarily appealing losses, which would be too much content to review.
I'm not sure that this is a big issue - Riot is comfortably in the black in its' books and would be able to afford some (key word, some) extra staff if necessary.
For players who go AFK during the game, there should be someway to detect if a player has displayed no movement for a certain amount of minutes at any point in the game and allow a remake...followed by a penalty for the leaver.
At what point do you draw the line? This already exists for pre-3 minute leaves. Wherever you draw the line, leaves will still happen after it. If someone wan'ts to "trollquit" or "ragequit", they'll just wait until right after the line has been crossed. Change it to 5 minutes? They'll DC at 5:01. Change it to 20 minutes? They'll go die at baron then quit. And it won't be changed to the end of the game, as it would just enable someone to "sacrifice" themselves for their team and leave to allow a remake and no LP loss.
Remakes are not designed for "ragequits" - period. They're designed for players who have legitimate issues opening the client for whatever reason that game.