If you do a lot of striping look into picking up a sprocket-fed plotter like a Gerber. They are awesome for cutting long striping.
I have found that how the vinyl roll is resting on the plotter rollers is very important for straight tracking on our plotters here, and using the spool holders really improves performance.
However, multiple long cuts like yours (15' ea x at least 6, right?) can cause the vinyl to walk a little bit, and with thin striping any little bit seems like a lot.