There is a KS statute which says both parents are entitled to parenting time unless the court has ruled it would not be in the child's best interest. Have a look at KSA 60-1616 (
http://kansasstatutes.lesterama.org/Chapter_60/Article_16/60-1616.html). So, something must have gone terribly wrong for you to have a "no contact" order. Where was your case heard and by what judge? Did the court make a finding that you are not a fit father for some reason? I've heard of drug-addicted parents getting more parenting time.
To answer your question, in my opinion, you'll have nearly a 0% chance of getting child support reduced or stopped just because you don't see your kids. In KS, they want to see that money changing hands if there is someone employed. You should have a better chance getting what is rightfully yours - time with your kids. I don't believe I've talked to any parents who have been completely cut out of their kids' lives by a judge. I'm betting something else was going on, the judge didn't like your attorney, or wanted to make an example of you or something. You possibly could have appealed the order. Your ex should at least have minimum wage imputed as her income level. That wouldn't reduce your support payment very much, but every bit helps.
It's not uncommon for the KS court system to look right through any efforts you've made to provide and what you've spent. Instead they simply want to see your paycheck subs and your 1040 so they can wring more money out of you.
After reading through some opinions here, let us know how you think you'd like to proceed and maybe we can provide more input.