I checked this morning and the side to side movement is present on the middle chainring as well at the same spot. I pulled off the cranks and rotated them 180 and the same movement occurs at the same spots.

I went out for a ride on a quiet road and realized the noise was present on a cog that is nowhere near rubbing when I stopped to check. At the spot where the chainrings move inward I get a ticking noise (Almost like a ratchet wrench). I think it may be the chainring teeth rubbing on the inside edge of the chain at this spot, The teeth weren't center in the chain and leaned to the left in this section when I checked. When riding uphill I realized the noise was a lot more prevalent, I can hear it better at a slower speed with less wind and tyre noise. It's also my understanding that a chain is under more constant tension uphill?

Could I be hearing the chain and chainring rubbing together under tension where the rings bend inward? That would explain why I can't hear it off the bike and pedaling by hand. The chain seems to be a KMC and has Zs and 8.3 written on it. It probably has about 2000 KM on it and the teeth on the chainrings do look a little worn.

I think I'd rather just replace the cheap cranks rather than fighting to bend them just right. My bottom bracket is a sealed square taper. The only writing I could find on it was TB702-2N L:120 C:28. There doesn't seem to be any sort of play in the spindles.