So when I go into the final chapter of Waking Dreams (after getting all the books in the other chapters) I find that the gate is shut. This is the gate right before the word of power for the dragon aspect shout and where you ride the dragon. I've tried everything and no luck getting it to open.

Dear PhilDante

please just watch the video from the 7th min onward .....https://youtu.be/ANp00jDxV6Y

its just right after you place the 4 books on the stools......and you enter the next chapter, .........the doors should be open by DEFAULT and will only close after you entered the combat arena

so it sounds like something gone wrong here, if you where smart to have a save ..........just reload and do it again ..........yea its a massive quest in time ..........but it far better than never finishing it

PS ........and if by any chance that you have altered the time-scale ...........your stuffed .......try and remove any mods that do so or set any INI manual changes done affecting time back to there default value witch is 20

What do you mean by altered the time scale?