That box is your problem. Not only is it complete garbage, but it processes 240p as 480i, so it will always look terrible, no matter what you do. You need to have realistic expectations with it.
Getting an OSSC or Framemeister that each have a built-in LPF will be a massive improvement over this. If you don't want to spend that kind of money, get a cheap consumer-grade CRT. The results will be light years better.
...all of that being said, the Genesis can still have noisy output. If you're looking for perfection, you still might need to do an RGB bypass to get rid of the jailbars...but they'll be MUCH less noticeable on a CRT.
With all due respect, you can't get what you want without spending money or a lot of effort. It's better to just accept that and follow the solution that's easiest for you.
Edit: Actually, if your TV supports 240p via component (and processes it as 240p, not 480i), getting a SCART to component converter might be a great solution for you. You can check if your TV is compatible by using HDRetrovision's test and a composite video cable:
Is your TV 240p compatible?:
http://www.hdretrovision.com/240p/#test
Does it process the image as 240p or 480i (scroll down a bit):
http://www.hdretrovision.com/240p/#problem