The thing is Jennifer, don't let your pieces become right angles. If the do, just cut them straight. As soon as you make a right angle, cut the corner straight and you'll avoid the right angle. Some of my friends include right angles for interest, and then as you suggested, hand applique over the top. Nothing wrong with that either! Remember with crazy patchwork, the rule is...... there's no rules.
Have fun.
Cheerio for now