My issue with a "Common Core" is that there is not a "Common Core" for all arts. Sure, there are a bunch of arts that study very similar katas / forms. But that list does not include all martial arts.
The "Core" of an art is the stuff they teach you first... for the first 6 months to a year. For Judo, Jujitsu: falling, Karate: stances, Aikido:blending, BJJ: ground fighting, boxing: footwork... These are not the same or common at all. If you went to a BJJ school, but had to learn a karate front stance, back stance and 3 katas... all that would do is hold you back from learning BJJ. The stuff they teach first, is the base they need you to have, to build on. As you build, your base gets stronger, better and more technical.
Heck, Iaido might start by learning to properly hold, care and transport your sword...
If you are worried about having certificates that mean something, find an art with a large organization. Make sure you agree with that organizations method for handing out certificates. But, in the end you have to realize... outside that organization, it really means nothing. The best you can do, is to be honest with yourself and with your students / prospective students. The best instructors I have ever trained with, in many arts, usually turn out to be the humblest people I have ever met. They realize that they don't need to hide behind a paper or belt or organization. They also realize, their are other people out there also doing really good stuff... and that there is a lot more to learn.
This does make matters a bit harder for the newbies. But the best thing we can do, is to be honest with them. They might not know much about the arts... but most people will eventually smell out a rat. (some sooner than others) By being honest about who and what you are and what you offer, you can help potential students find the path they are looking for. Hopefully, they will eventually appreciate your honesty and help.