Here was the set of tiles that I had at the end:
ADEEEGGHKLLMNNNNOQRRRRRSTVXYZ
I decided to save the tiles and try to work out a solution later. I spent some time working on this problem on two consecutive nights. The second night I found a solution that used all the letters but one N, but that seemed to be the best that was possible.
Finally, several days later, I found a true solution. It's possible to vary some of the peripheral words and get alternate solutions, but there is a core structure that I have not been able to alter without rendering the grid uncompletable.
This puzzle can be solved without using any two-letter words or any vowelless words. (I think that violating these constraints would make the puzzle too easy.)
I leave this as a challenge. I will post a solution at some point in the future.

![If I stay there can be no party. I must be out there in the night, staying vigilant. Wherever a party needs to be saved, I'm there. Wherever there are words that need anagramming, I'm there. But sometimes I'm not because I'm out there in the night staying vigilant, watching, lurking, running, jumping, hurdling, sleeping. No, I can't sleep. You sleep. I'm awake. I don't sleep. I don't blink. Am I a bird? No. I'm a banana. I am Bananagrammer. Or am I? Yes, I am Bananagrammer. [applies chapstick]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgI5Yf53B1clpF3cLb11zYrIhaMn1Grv8uDvAhy_9vwjTU-CZCcX5MYmPwX-TnSagBaWwvJpIWeVsOP3q4r6k_HYnuRcVAOou4fwCkkVU7Or2NXmaWfZS6CjtkPnaeIdq3-wvdOC2DJb-Ra/s400/BGR-plot-medium.png)
