Can't speak for most of your post since I don't really play with Kururu or Nat.
High _______ Beta/Gamma/Alpha tunes are the most effecient, yes. It's just simple math.
The two highest WLK breakpoints for LND are 32 / 36. The highest WLK breakpoint for non-LND is 35. These are not Boost Run breakpoints which are very different. Please also keep FLY at at least 1 so the bot can actually climb terrain with the spacebar.
The FLY breakpoints are 25, 28, 31, 34, 38. The bot has to be a very strong alpha bot or long ranged bot in order to make 25 and 28 FLY acceptable. Otherwise aim for 31, 34, or 38. Please keep WLK at at least 1 so the bot doesn't take too long to properly land on the ground after flying.
Tuning TGH is not advised. First tune mobility (WLK/FLY), then weapon tunes if needed, then TEC/STR, then possibly HP. 40 TEC / STR may not be as mandatory these days since they revamped the hit system to be more merciful and your damage goes down quicker if everyone is shooting at the same guy, but if you find yourself fighting 1v1 more often or if you're aggressively hunting down guys to kill, 40 of a damage stat is still good.