How do I balance art with business demands?
It's all about prioritization. What is my goal? What do I need to do to achieve it? Rank those steps. Get 'em done and drop the ones at the bottom of the list that don't fit within the time constraint.
Kind of a glib answer, eh? Lil' bit...but then again, not so much. I've been doing this writing gig for more than a decade. I've learned lots of stuff (as one would hope, no?). Among those things are what external demands can be declined/ignored, how long certain tasks take (time needed to write a book is not among that lessons, alas!!), what tasks can be done by others (and for what costs), and what stuff will bite me in the ass if I don't get it done by a specific date.
My goals change as I achieve them. Timelines shift as my skills improve or as new strategies develop. Plans blow up as life happens. Adjustments are made. The most important thing is to not sacrifice your mental or physical health. Set realistic goals. Push back when necessary. Ask for help when needed.
Be motivated, not guilt-driven.
If you owe someone a deliverable and can't make the date, for gods' sakes, let them know as soon as possible. I know it's hard to admit you're not perfect, but it's always easier for everyone involved to make adjustments when given the time and space to do so. Oh, and if you do need to request an extension, build a few extra days into that new estimated date. Don't short-shrift yourself out of shame! You're already taking the hit for one extension, and you don't want to relive the drama when asking for a second extension.
P.S.: This strategy applies to life in general too.