Here's the real way to climb when we get a real solo que

Find 1-3 OP champions that aren't permabanned and don't have many autolose matchups. Learn everything about them. Acquire ELO. Riot has too many champions for them to possibly balance with all the compositions there are and the myriad of items and rune/summoner spell configurations. And besides that, they're continuing to add more champions at a fast pace so there is no doubt that you will find the proverbial gem in the rough if you look a bit. What you see in LCS is only a small subset of what's strong and it's also usually what Riot reacts to the most when they make balance changes.

You can also pick champions known for being strong (see Tier lists) but that due to the ban limit usually go through. This is the truth from looking at profiles of many high ELO players. They usually are ahead of trends or at least pick strong champions. I'm not just talking about avoiding off-meta stuff (although that usually seems to happen more in higher ELO) but out of the dozen or so ADCs, the top ranked players usually all alternate between only 5-6 picks. Yes, you can climb with anything but it's going to be harder without this approach imo. There are certainly very diverse players too like imaqtpie, nightblue3, voyboy and I'm sure many others but it takes so much more experience to pull it off.

BTW: I think Riot is realizing that their roster is growing faster than the ability to balance it. That's why they're pushing dynamic que so heavily. While it's fundamentally flawed due to a lack of consistency between player pools, until very high ELO, champion power picks should matter much less. The extra communication and strategy will be much bigger factors than in solo que and thus the picks themselves will be relatively less important in deciding the outcome. This isn't to say that balance is any better, just that it's a variable with reduced effect so poor balance won't create as much frustration in the player base as it normally does in solo que.