Looking for Ezreal ADC Guidence

After watching Faker play Ezreal mid I realized that if you are fairly good at landing skillshots, ezreal could be a very strong pick for you. I am no Faker, but i land a good portion of my skill shots, yet I can't seem to carry as Ezreal. This is not another "im bad but I refuse to admit it" post. Well mostly. I lost 9 games in a row as Ezreal adc, but the worst part about those 9 games is that I had the highest damage output on the team, highest damage to champions, and was positive in kills. Many people would say "oh my team sucked" but the only common factor of these 9 games was my Ezreal, so i figure its at least partially my fault.

I think the main issue was that I couldn't dish it out fast enough. The q's hit hard, but if I came in to put in the supplementary autos, I get focused hard, and I would then be forced to kite the tankiest person on the enemy team. Seemed like I only made a huge difference in long drawn out fights where I did not have to commit, but I can't really expect fights to go that way... ever really. Despite still getting kills and doing damage in short fights... idk what i'm doing wrong.

For those of you that manage to carry and win games as Ezreal, what do you recommend? Team fighting doesn't really seem like the way to win with him, but as an adc he is obligated to be there.

I guess where i'm going with this is, is Ezreal not good enough in a meta where everyone is beefy, and you can't isolate anyone squishy enough to dual them? Maybe he is supposed to be a split pusher, using his blink and iceborn q's to run away? Advice appreciated because it hurts the soul to do so much damage but not be able to carry.