When you say you have the pinch hitters set, is it the platoon PH via the lineup function, or the PH setting vs R/L in Team strategy?
Could also set Jeffcoat to be a pinch runner--it may cause HAL to reserve him for that role and not use him defensively.
As silly as it sounds, sometimes can tweak those combinations to limit HAL's options. Like selecting Davis as the platoon PH for his own position in LF on all lineups. Or as Chris said re: defense.
And try ensuring any platoon PHs are not also fulfilling a role as a strict PH vs in the team settings simultaneously. Have seen that go weird...but if you already have that set, then maybe switch away from it and disable 1. Trial and error unfortunately.
Also assuming the hitter settings for davis you have set as Do Not PH for, do not PR for,etc and all the rest as mentioned. Some of it doesn't make sense, but HAL's decision trees sometimes cross branches the way the business rules are written.
Unlike Westworld robots, I don't think HAL has a core directive, except maybe, "when all else fails, find an obscure way to befuddle a manager"