I became an independent consultant and directly competed with the services arm of a software company that I had previously worked for (and had an outstanding NDA with). I made sure that the contracts for my company were for training, coaching, policy, standards, rather than just being a tool jockey for that particular software application. I also called the president of the software company and let him know when I had a contract coming online where his product was installed. He appreciated it, and even though OF COURSE they were hiring me for my expertise on that software product, that wasn't the ONLY reason. So I think I just tried covering the bases.
My non-compete covered doing the same type of work. I just made it so I was doing different work.
A few years after going out on my own, they actually hired me as a consultant to go and support some of their clients. Part of their contract included that I would always in any future work, advise them when I accepted work with a company where their product was installed. I agreed to advise them ONLY IF the company in question was also one that I had supported when representing the software company. In other words...any new business was mine and I was under no obligation to tell them anything about it.