How do I include a journal article draft in my dissertation?
This is actually how many "sandwich thesis" dissertations are actually structured, my own included. Generally speaking, I've seen them structured like so:


Background, literature review, sections on data sets, and other material that will matter to each and every chapter under consideration, and is likely more detailed than you would find in a paper.
Each "paper chapter" essentially existing in it's free-standing, ready to be published form.
Final chapters putting those free standing chapters in context with each other and your work as a whole, summarizing key findings, etc.


So basically, the short answer is to put it in as a chapter in its current form. I've never seen any journal object to a paper having previously appeared in a dissertation, and keep in mind it may very well change - there will be editorial comments from your committee, reviewer comments, etc. It's essentially just a pre-print.