Fastest way possible to climb (Goal: Silver 5)

Yo guys, (sorry for the long following introduction) so I would like to get out of bronze this season, I've set a goal that says I wanna be in a new league every season, yet I'm still bronze in S7, looking to change that. I am willing to play the most boring fucking champ 250 games in order to get out of this hole. I'm not even your typical rager and so on, my mindset is completely ok, but at rhis point I'm getting slightly desperate. So I've been watching lots of LS lovely content. He tells you to play Annie mid and top. I'm willing to do that if that gets me the elo once I've gotten good at Annie. I've followed his tierlists and so on but I'd much rather play Annie only if that actually makes me get ou because it's easier for me to focus on one simple strong thing. (I have optimal runes, masteries, decent laning knowledge)- Keep in mind I wanna get out without some Kayle/Yi duoQ or some shit

All I'm basically asking is if there is any possible way to get to silver 5 by the end of the season quicker than playing Annie Top/Mid (my main roles) I don't have enough time to be a meta slave btw. And yeah I know that no matter what I play I will lose about half of my games, but I just need the best odds to fly out of bronze.

Thanks in advance (I know this post is a huge mess and I made it complicated, but I want you guys to have some background knowledge.)

I linked the LS video I'm talking about.