My sons both did extremely well with a 6-250 with a long barrel which did 2 things:
1) provided weight against recoil
2) put distance between the muzzle & him to protect against blast
I actually think that #2 matters more than most people recognize.
He used very mild loads with ballistic tips. With low velocity loads I’d stay away from Barnes and use something that has a wider range of effective velocity. In the 6.5 the 100 GR Hornady tipped target bullet would be a great candidate for you.