I'm not tracking with the "ideal geometry" concept. 25 caliber itself doesn't have any magic BC properties that give it a better weight/BC ratio. Larger caliber bullets will have better BC when scaled for weight. But beyond that the only thing you could attempt to claim is "I designed a superior bullet shape with better BC than Hornady/Sierra/etc".
As far as being in a PRS/NRL sweet spot for recoil, I'm not sure it is for the majority of shooters. Most guys are 6mm, with a strong trend towards lighter recoiling variants. The upper end of 6mm recoil would be a hot load in a 6 Creed running a DTAC, but most guys choose to run smaller cases, lower velocities, etc. Realistically, your recoil with a 131gr bullet going 2925fps is MORE than a conservative 6.5x47 140gr load going 2750fps (but better ballistics). Alternatively you could do a DTAC at 3050 fps from a 6 Creed and match the performance of the 131, and do it with with noticeably less recoil (but worse barrel life than the 25 cal).
Ultimately it's another rung on the sliding scale of ballistics/recoil/barrel life. And a claim of "Goldilocks" is in the eye of the beholder.
Let me try to make that statement more clear. I decided that FOR ME the recoil of 130-140 grain projectiles at 3000-3125 fps was all I wanted in a match rfile. Taking that bullet mass and a certain speed bandwidth resulting in a certain amount of recoil I knew I needed to see which diameter would result in the highest performing projectile. This coincided very near 257.
I'm not going to get lost in the weeds about surface area:mass but you at once said 25 cal does not have any special place in that range but also state the heavier you go the BC increases. I had previously stated that 25 cal allows for enough mass to have a great BC but simultaneously doesn't prohibit muzzle velocity due to being too heavy for non-magnum short action cases.
I can factually state that the 131 ACE is more efficient than Hornady, Berger, and most Sierra's in the right circles, but due to the attitudes in this thread it's not the place to be doing so, despite the facts of performance and form factor.
Matches have gotten shorter over time as the 6 grew in popularity and hits were not being scored or seen at long ranges and 6mm is generally the king for how matches are shot now, but we didn't design and execute this business to beat 6mm at short to medium range trajectory. I have a few killer 6mm designs we will eventually make if other MFGs do not, but that is for another day.
The high performance 25 cal bullets that exist and will exist in the future will blend the barrel life of large diameter calibers and available BC with the speed of a lighter bullet.
Considering performance out of a short action vs recoil, 25 cal is and will be in the Goldie Locks Zone for hit probability and increased energy at longer ranges to 1500-1700 yds and a great low recoil high performance for low recoil medium game hunting to ethical ranges. These statements are simply based on performance #'s.
Define balanced performance however you want.
For me, 0.345 G7 at 3050 fps in 2.880" magazine using standard boltface cases with 10 lbs of recoil and higher kinetic energy than any 6.5 standard bolt face short action - that is quite indicative of balanced performance or a Sweet Spot.
If it's another notch on the sliding scale, it's quite a decent notch for hunting and for fun shooting steel to over 3/4 of a mile.