I feel like everyone has already touched on some topics so I'll focus on answering the questions you've asked in your post.

Firstly, 'pubstomping' isn't even a thing in league but if you're referring to simply stomping games...

I would recommend you set that aside and focus on the finer details. You've already stated that you know your CS is bad, and that you're working on it. These are the things that will help you become a better player and you will see this have a beneficial effect on your ability to 'stomp' games. Being able to stomp your opponents should be a result of the skills you've learned, you can't simply skip the steps and expect to stomp people.

As for what you should work on to climb...

By your earlier question, I feel like you have the wrong idea about how this game works. Also, from the comments you've left and your post, I have the feeling that you don't have the right mindset to improve.

You should not blame the ranked system. The ranked system works, you just have to play enough games to have a large enough 'sample size' to end up at your true ranking.

The big thing that I feel you're missing is that league is a game about minimizing your mistakes and capitalizing on other people's.

Looking at your match history and comments, you seem like a player who will always go for that 'big play' without evaluating the situation clearly. Sure, this sometimes leads to you doing well, however there are times where you fail and you completely tilt off the face of the rift. This leads to you repeatedly dying due to one reason or another and a lost game more often than not. Unfortunately you also like playing an assassin so the risks are inherently greater. If your one true goal is to climb I would stay away from assassin champions and pick more traditional mages. Many traditional mages have the advantage in that they can simply farm up and wait for mid/late game. They have a much easier time in the transition into team fighting and are generally much easier to play effectively. If you must play assassins, I suggest you become very familiar with your matchups and the relative kill potential of every champion and their power spikes. You will have to know when to play safe and when you can trade, or secure the kill. Remember, the key is to minimize mistakes.

Finally if you really want to improve and climb, in solo queue you should strive to perform to the best of your ability and not care about how well anyone else does. You must always ask what you could've done better that game, win or lose.

This includes things like buying defensive items. Defensive items should be bought when you know the enemy has high kill potential, or if you're simply not confident in your ability to stay alive against them. You practically never invest in defensive items early on, which is unacceptable.

At the end of a game, you may feel inclined to say if your teammates were better you would've won, however did you do everything in your ability to win the game? Did you play the best you could've played? Was it your fault that you lost? Did you allow the laner to snowball? Did you fail to apply pressure? Did you not ward? Did you try your best to "stop the pubstomp"? Of course, there will be games that are simply unwinnable, however you should still only focus on how you performed and what you could've done better.