I had a finnlight that had a bad barrel. Sent it to Beretta and they said it was fine. If I shot it scalding hot, groups were excellent. Otherwise, groups were all over. Replaced the barrel, pillar and glass bedded in a McMillan and not it's a shooter.
The 85 has a unique bedding lug and a cheap, flexible stock. My point is, it could be one or more items, poor bedding, contact with the stock, or a bad barrel. Even custom barrel makers have dogs. Before you invest in parts you might want to 1) ensure it's free floating, 2) check for wear marks around the lug to ensure the stock lug is mating well with the boss, and 3) have a another shooter shoot it and see how it groups. It could be an easy fix before investing.
Also, I found the stock barrel to be front light on balance and harder to maintain good form while shooting unsupported. I really had to focus on technique to ensure I didn't cause a flyer.
All the other recommendations are on point, but you may want to eliminate the other areas first.