I'd stick with the soaking in hot PBW and high water pressure to try and unclog it. Something about drano just sounds wrong...
Stick it in the oven and set the oven to clean. Then just backflush the ash out.
I wouldn't mess with draino...there's all different types of it. Some are enzymatic, some are basic, some are acidic. You can probably find strong acid at the HD. I know I used some to etch concrete, etc. Again, don't do it if you don't have the training or equipment necessary.