I went through exactly the same thing years ago, when transitioning from English teaching to design. I assume you're on the "Specialty in Humanities & International Services" visa, like I was? As far as I know, it's totally no problem to work as a designer while on this visa...it's just a matter of managing to renew it.
I've "self-sponsored" a number of times, so it's certainly possible. I never really worked out what the specific "rules" are (even the immigration lawyer I dealt with told me they're a little grey), but it's basically as simple as proving you're earning a certain amount of income each month (I believe it's around ¥200k/month, but may have changed), and that you're paying your taxes. To prove your past income I think you can just show invoices up until the point of visa renewal application, and to prove upcoming income, you generally need to provide current or upcoming contracts with clients, or even just letters from clients saying "We need Christopher in Japan to help out with our company etc. etc.". Again, I'm not entirely sure of the exact rules, but I never had any issues.
The immigration lawyer I used multiple times was called Yoko Majima, from June Advisors Group (www.june-group.jp) -- I'd recommend taking a look at this page in particular, which gives some more information on self-sponsorship:
I'd also really recommend asking her for help if you're unsure how to go about it--for me, the cost was well worthwhile, as I managed to get a 3-year visa renewal right at the end of my first year in Japan, then another 3-year, then a 5-year. I'm now mid-application of my permanent residency.
Hope this helps! And nice illustration work, by the way!