Drywall over irregularly spaced studs - how do I secure edges?
The edges of your drywall pieces must be on studs - at least two of them and preferentially all four.  (some drywall guys will vastly disagree with needing 4 so not trying to start a war)

But two is a must.  Your drywall should end on stud or be butted up in the center with another piece of drywall.  Either cut your drywall or add more studs.  There is absolutely nothing wrong with 17-19" on center which sounds like about 3 studs per sheet.  I have run into this with old houses.  Just buy 15 2x4s and throw them up where you need them.