I'll have to disagree on what PH's (at least some, anyway) say about the current Barnes crop of bullets - especially for heavy thick skinned animals.
My outfitter for an upcoming Naigai hunt in S. Texas recommends Barnes over anything else - based on years of experience. Nilgai bulls are big (up to 600 lbs), thick skinned, and very hard to put down. Plus shots can be on the long side.
I'm loading a 338 210 grain Barnes TTSX at 2,900 fps and hoping it does not open too quickly!
My DG PH in Africa also preferred Barnes - at least for the 9.3 and 375 calibers. (I used Swift A-Frames, but would choose Barnes if I have another opportunity).
But regardless of bullet type, if shooting the same weight (225 grains in this case), every 338 bullet I've referenced has a higher BC and SD than the corresponding 358 bullet.
The updated TKO math used by the OP is at the muzzle, btw with no regards to retained energy at some normal distance. Also it has no allowance for SD.
Also, my understanding of TKO is it was used primarily to compare different bullet weights of the same caliber. I read that on the internet so it must be true.
But sure, if hunting smaller thin skinned animals, the bullet choice should be matched up accordingly. Likewise for the anticipated distance.