This might help you.
http://www.rioproducts.com/fly-lines/shooting-heads-lines/heads/t-8-11-14-17-20
If you notice, all the the factory heads start out at 30' in length so you can cut them back.
Most fly shops sell the Rio T material in bulk so you can make your heads yourself and just add your own loops.
Lots of variable such as current, length, material type etc come into play how fast a head will sink.
The problem with using short heads on a shooting head system is they will have a tendency to dump.
The LC in Cortland LC -13 stands for 'Lead Core". The Rio heads are much more supple then the LC-13. I used LC-13 for heads while fishing bluewater before Rio's T lines came out and it worked well.
I'm not sure how it compares to lead core trolling line, but it might be worth a try.