I'll make a 100% guarantee that your data will be flawed.
I'm an anti-Elo-hell-guy myself (if anyone is interested in my bias). I don't believe in it whatsoever. Now, from what I can gather, the OP doesn't seem to believe in it either and my be trying to prove what happens to be my opinion to be right.
But the fact of the matter is, you can't possibly see all of the data you need to see.
Here's some comments and criticisms for you.
1) In regards to Swift Hikari's comment, it would be great to have an objective 3rd party looking at LoLReplay with you. This would help make sure you're judging your own play fairly. However, it would not be appropriate, in my opinion, to study "Elo Hell" while duo-queuing. Duo-queuing effects a number of factors, a LARGE number of factors. And in the end, people will be prone to point to your study and simply say "Well yea you can get out of Elo Hell by duo-queuing! No one doubted that!" The majority of the complaints seem to be "There's no way out of Elo hell unless I duo queue with someone from a higher bracket." I can explain the problems of duo-queuing for this study more if you're interested.
2) This should have probably be the first point, but it's not, oh well. You need to define "Elo hell." You need to define it in your blog. You need to probably define it in your post here too. I could tell you that I'm going to disprove magnetohydrodynamics. Open a blog, make posts for a few months studying it, and then in the end, say "There, I've disproved magnetohydrodynamics." If you know what magnetohydrodynamics is, then maybe we're on the same page. But if you don't, you didn't get anything out of my supposed study. And the problem with "elo hell" isn't that no one that'll read your blog has any idea of what "elo hell" is, no. The problem is that everyone has a different definition or opinion of what "Elo hell" is, so you need to state YOUR definition of "Elo hell" so that your readers know exactly what it is that you're disproving. If you're going to claim this to be a "case study," you need to be very clearly on exactly what you're studying and what you're attempting to prove or disprove: very clear.
3) You won't gather all the data. It's impossible. The argument from the people who believe in Elo hell is always that they always have the raging/feeding/trolling/general obnoxiousness teammates on their team and that that puts them at a disadvantage. The argument from the people who don't believe in Elo hell tends to be that yes, sometimes the raging/feeding/trolling/general obnoxiousness teammate is on your team, but assuming you're not that player, he's actually on the enemy team 20% more often. Now, this is a statistical fact. And there are numerous ways of proving this statistically. But to the people who want to believe in Elo hell, the statistical facts don't mean anything to them. Your case study WILL show how frequently the raging/feeding/trolling/general obnoxiousness teammate is on YOUR team in your given Elo range, but as you can not see the enemy team chat, nor can you rely on enemy players accurately informing you when this behavior has taken place, there is no objective, empirical way of measuring how often that player actually does end up on the enemy team. Now, sometimes the chat will spill over into ALL chat and you know then that they have that behavior. But you can't assume anything about the times you don't see that behavior in ALL chat. You can't make a guess one way or another about how frequently it is happening.