Yeah, I'm pretty convinced the optimal Awoken Ra shell is Ra/white Kali/white Kali/black Kali/???/Ra, and the last slot has to be blue/green (or green/blue). There aren't that many things in the game with those colors, and a large chunk of what we do have is either JP-only or is an orbchanger that makes activating Ra impossible.
Options include:
-Top Droiddragon
Pretty crappy. Bad stats and nearly useless active on an extremely long cooldown. A case could be made for him in a lot of dungeons to block pre-emptive poisons and jammers, but since an ideal Ra team is stacked with board changes already it would have to be a pretty weird dungeon for that to be necessary.
-Awoken Orochi
Could work. Has a ton of skillboosts and a time extend, and his active will be up extremely quickly because you'll have a billion skillboosts. The problem is that he needs prong matches to actually do damage, and that should be extremely low priority when you're figuring out a board. He's also not compatible with the x2 from Ra's leader skill, making him hit even less hard. But his HP is huge, which actually might make him viable despite his feather touch-tier damage (because frankly none of these options will be hitting that hard compared to your white damage).
-Awoken Isis
Definitely one of the best-case scenarios. Useful utility skill that can also just be spammed to trigger Ra's leader skill, has the highest stats of any option by a tiny margin, isn't incompatible with Ra's boost. How useful the shield or bind clear actually is varies by dungeon, but in my opinion mostly they're not that necessary since you typically have the option to just burst past anything that's going to bind you or hit you hard with an active. Can be useful against pre-emptives for sure, but with Isis 4/6 of your team is bindproof anyway, and even if your two white Kalis get bound you still have all your colors. But that's okay, because her active could be completely blank and she would still be pretty solid.
-Soaring Dragon General, Sun Quan
Possibly my preferred choice (although I don't own and therefore have never tried Isis). I don't find myself in situations where I feel like I need Isis' active very often, whether it be for the bind clear, the damage reduction, or just to get my boost for free. Sun Quan's skill, on the other hand, is ALWAYS great. Delay is great, x2 attack for your Kalis is excellent. He has a few significant downsides though. His stats aren't very good, he's not a god or devil so he's getting less multiplier than everyone else, and he's not bindproof, which means the rare-but-important pre-emptive wood binds or pre-emptive water binds completely break your team's ability to do damage. Fortunately black Kali had bind clear now, but you need to have enough hearts on board to use it and it takes a whole turn.
-Armored Green Ice Knight, Muse
Not great, but situationally useful I guess. Bad stats, bad awakenings, but if you absolutely must kill something right away Muse is the way to go, because it basically will happen. Has decent HP (much better than Sun Quan) despite the low weighted stats, which is arguably the most important stat for a card that won't be a significant part of your damage no matter what you do.
-Apex Blue Flower Dragon, Starling
Not a good option by any means, but if you have nothing else he could probably fill the slot. Good stats, barely passable awakenings, and a skill that you can barely use because it breaks Ra's colors, but at least you can use it before a board change for a time extend. Being farmable counts for a lot. If I didn't have any other options I would probably use him over Droiddragon.
-Heavenly Fortune Goddess, Lakshmi
Another "if you really can't figure anything else out" option. Decent stats (although low HP, which sucks), acceptable-I-guess awakenings, and a skill that sort of does something, albeit on a bizarrely long cooldown. And you can't make Awoken Lakshmi if you make her, which sucks. But yeah, she's not unusable.