I don't know what people have against the occasional strap usage.
Nothing wrong with them when used sparingly.
But as far as increasing grip goes, check out Fat Gripz, they're humbling.
Also, towel chin-ups, grippers (CoC for the win), and if you're feelin' frisky you can try using your straps to IMPROVE your grip.
Lemme 'splain: you loop the parts of the straps that your wrists are supposed to go through over the chin up bar then you grab hold of the part of the strap that you're supposed to wrap around the bar and you do pullups while supporting yourself on the straps.