Game Remake is amazing, but it needs extension in timing

Hi! I've never had problems with getting into games, but recently I had to move into a new location and the internet here for some reason has a hard time connecting to the game sometimes. For some reason this only happens with LoL and I don't know how to fix it (did the client repair and all that jazz).

Now I love the Game Remake option, but when I keep getting constant "The game has crashed/Connection failures" I log into games late, like maybe 3 and a half minutes late at the most, I know this sucks for my team, but it's not completely game changing. This only happens about 1/10 games. Every time I see the end of game chat it only shows that the game has lasted only 3 minutes before the remake happened. What is really frustrating, a lot of the games I missed happened on the day the servers went down last week, and because of something that happened on Riot's end, I am now getting punished for it. I now have to sit in low priority queue. I know I cannot be the only one who has afk/leavers points against them because of spontaneous internet issues or server problems.

I am not saying that I or anyone else shouldn't be punished. There should be severe punishment for leaving games, but not for only missing a few minutes when the whole game is salvageable. But when we know we have disconnected or something has gone wrong, give us time, we are panicking as it is. I suggest giving the remake option available at 5 minutes into the game. This should be more than enough time to solve a problem. Punishing people for missing a few minutes because of something out of their control isn't going to solve the overall problem with leavers, it's only going to make the game more frustrating.