I think you can, indeed, make that cut and make it straight with a good quality, sharp, crosscut saw (e.g. don't even try it with a cheap or dull saw). You can cut slowly and make a nice clean cut (I've seen people rip 4 foot lengths using nothing but a crosscut saw).
Having said that, I can't find a flaw in kcoleman's technique, although you are going to need to get the guides secured well. As kcoleman points out, the outer edge of the vertical cut is where you need to be right on. So, if you have a problem with the inner edge, you can backcut with a coping saw to achieve that flush edge on the outside.
Cheers.