I do a LOT of straightline quilting, since I like the look. Here's my 2 cents...I wouldn't try this without spray basting, especially going from one edge to the other instead of center out...it would be difficult to avoid fabric creep. If the spray 'gets to you' then maybe use Elmer's school glue and drizzle.
I would also make a quilt sandwich about 30 in square and test this pattern out...it sound like it will look like a bunch of scribbles unless you make each line a double line about 1/4-1/2 in wide....so you get a kind of match stick effect. I could be wrong...it's just my sense.
One thing I did that was interesting and took a HUGE amount of thread was to begin a series of straight lines going from the center to an edge...I did maybe 30 lines, close together. Then I made another series of lines at right angles to that first series and went from the middle of the first series all the way to the edge of the quilt, so all of the lines together create a kind of diagonal effect..it looks really good.
hope some of this helps.