The 3 PH is rated to lift 680 pounds 2 feet behind the lower arm balls. A forklift is likely 4' long (or so). That extra length will severely limit the lifting ability.
The mower shouldn't make a difference unless it is at the top of its lift and the hydraulic pump is in relief mode. If it is a mechanical lift deck then it will make no difference at all. Same with the FEL.
This topic will get more responses in the Kubota Owning/Operating forum. Maybe the moderators will move it.