Problem with climbing

Hello, im playing league since S1, and i actively avoided ranked in seasons 1-5. I just played few games to get my gold ranked rewards and that was it. I started playing solo ranked in S6 and continued in S7.

In S6, i peaked in P2 (with 61% overall winrate), here are stats from my 2 accounts: http://i.imgur.com/RVNTnf8.png

This is me in S7: http://i.imgur.com/NK3FPkG.png

Problem is, after season reset i was placed into Silver 4. I tried to climb, but it's... extremely slow. I mean, i have low/mid plat MMR, so im playing against players WAY above my division. It's okay because i get significantly higher LP gains (around 30) and really low loses (-8 max). This means i am able to get 100 LP in 4-6 games, so it's really fast. However, it all falls apart when i reach promos. Promos don't care about my MMR, so i HAVE to win 2/3 games to get promoted. But here's the catch, im playing against players MUCH higher than my current division!

Getting 2/3 against high silver/low gold players would be really easy and i would climb quickly. Getting 2/3 wins against plat is MUCH less probable. This means im often failing my promos, which sends me back to 90LP, and requires me to play 3-4 more games to get NON-GUARANTEED chance to get ONE division higher.

This means very high MMR considerably slows climbing, which is obviously very flawed. If i were matched against low gold, i could steamroll my promos and gtfo from silver/gold.

So, if i want to climb i have to play ridiculous amount of games because promotion system is really flawed. This causes burn-out and i simply don't want to play if im not getting any higher. It would require ridiculous amount of time that i don't have. If every game took 30 minutes, i would need MINIMUM of 30-40 hours of playing until i get close to where i belong...

Edit: This is how my games look like: http://i.imgur.com/5rondqD.png