I'm not getting into theory fighter territory. I HAVE played a good chun. I did a ~50-game set with DMG.Ludthinks, and while he's primarily a tourney SF4 player, he takes his marvel chun seriously and taught me a lot. I've also played long sets with a good Joe/RR player(Boy786/TGYMK), and other strong Joe players(Family, LPZ), so I know what he's capable of in general, as well.
I'm just saying, from an experience I've had with the characters standpoint, that you're selling High Level Chun a little short I think. She has good confirms, okay movement, the original TAC infinte, good mixups off blockstrings and good damage, she just lacks ranged options and oppressive normals. She's pretty mid tier.
Would High Level Joe + Assists have an advantage? Yeah, sure.