Your 513 is built on the same action as the 452, so I assume the trigger is the same as well, but you should verify this. On my CZ 452 American, I used the Brooks trigger mod to turn that crappy trigger into a crisp lite work of art. It makes a huge difference and has selectable trigger pull weights to meet your personal needs. It takes about 15 minutes to install and is really easy to do. Here's a link to his website:
Eric Brooks Website
You may want to drop Eric an email and ask if it will fit your 513 before you order.
On a side note, I found that my 452 really loves Wolf MT or ME ammo. You may want to start there with your testing.