Edit: Problem Solved, solution posted at bottom
I'm going crazy trying to figure out why this is happening.
This is well known issue, and I've done everything recommended so far.
I'm using php version 5.3 and magic quotes are off.
This issue only occurs when using the plugin wp_blocks, so I'm assuming there is something in the code that is making this happen.
I'm currently sifting through the plugin to see if there is anything that would force this behavior.
Of note is that if I insert the html entity ''' and then save and go back into the html (I use ultimate tinyMCE, which has a nice highlighted syntax editor, but this also occured before isntalling that plugin), it will replace all of ''' with apostrophes.
The plugin used only a wordpress function called wp_kses_stripslashes, which only works on double quotes apparently. I simply further processed the passed data through stripslashes and voila.