Its not really a punishment. Your MMR dropped to low to be representative of the Tier. Your 3 win gain for going 9 to 6 is going to Add more MMR back to your account. Keep it up and your MMR will be fixed and your LP gains/losses balance out. Once balanced your 9 to 6 would be net LP gain.
Its really not complicated. LP moves slower then MMR. If your above and get to high your expected to cost your teamamtes games so your MMR will start to decrease. But as your MMR is > Tier your LP losses per loss are lowerd. With time it will automatically balance out to have your MMR and Tier be representative of echother.
Your currently dealing with the opposite. Your MMR is below your Tier. So it expects you to beat weaker players and is trying to zero in on the division that's representative of your skill.
Also MMR is ment to be a range and part of that is why its ok for it to wiggle around every game. A MMR value represents the expected average for a player. It expects you will have better games and worse games, and that this will vary for player to player. The point of the MMR system is to move players to a range where they don't negatively impact others games as much. the main flaw is its inherently easy to try to lose. Any one can make it to the bottom. So match maker from the starting tier and down suffer because any one ever can aim to lose. Yet its great for a competitive ladder because even thou some higher tier players can and will troll a weak player playing to their very best is still so outclassed they are incapiable of making it up. End of the day Weakest players sink and stronger ones rise.
How to climb is again really simple. Win more then you lose consistently. Currently... you as a player are not. Fix this and your going to climb. Win rate is honestly the only thing you really need to care about. Do I win more then I lose playing X in my current MMR.
Set a value where you check your %. say Ever 10 to every 20 games. Decide if trolls or bad luck skewed your %. Adjust it. Decided after do I keep playing X. Winning lane 100% of the time and losing 100% of your games is bad. You cant climb. Losing lane 50% of the time but winning games 75% is climbable.
Stats are good for knowlage. But stat padding is easyer then trying to win. Spam any and all abilitys when ever you have a target regardless of if they make any real impact and you end up with higher Damage and CC scores. But its not inherently helpful.
spamming R every time its off cd will have a better CC score. But the one who saves it and cast it smart to make a key engage can win a match for her team.
Padded stats are useless, as again All you have to do is so simple. Win more then you lose.
(don't get discouraged by lp. Don't trip out over tiers. Play to win. Check yourself. Focus only on your self. Seek to improve. Don't tilt.)