IMHO, everybody gets stuck on big, Big, BIG. My hunting partner shoots a 243 with a 90 gr. pill. Do not know exactly which one every time, Nosler Partition maybe, and some Sierra stuff, and they shoot right through necks, rib cage, shoulders, etc. I have killed deer with his 243 and a 90 gr. pill. Hogs too!
A 308 caliber bullet, whether pistol or rifle origin (is there really a difference? Bullet shape maybe, but not in bullet construction), should work great with the right powder and inherent velocity.
I went to the Hornady web site and found no XTP for the pistol. The only one was a 30 Mauser .308 x 86 gr. RN ($19.11/100); BC 0.105; Sectional Density 0.130. I looked at the rifle bullets and found the lightest was a 0.308 x 100 gr. Short Jacket ($18.53/100); BC 0.152; SD 0.151.
Are there better rifle bullets for the .308? Sure! Are the two herein "close" to one another? IMO, sure!
High velocity, flat trajectory, brush busting, etc., are great, but not the point for the lady. I kill hogs with the 22LR rimfire. The world record Grizzley bear from 1953 until the mid-1980's was killed with a 22LR single shot. Whould I go Grizzley hunting with a 22? Hell no! IF it was all I had at the time and I needed to defend myself, it is enough gun provided the bullet is put in the right place the first time.
Bullet PLACEMENT is the real key. Confidence in one's ability and thorough familiarity with the equipment is the key to bullet placement. For the lady, recoil, velocity, trajectory, etc. are all going to be moot if she is flinching.
Oh yeah, and a steady rest. Shooting off hand should be avoided as there are just too many good rests available not to use one.