Well your old Gleaner "K" had one small steering cylinder and weighed about 1/3 of your JD 6620. You should have the heavy rear axle that has two steering cylinders. The steering motor (JD calls it the steering "PUMP" on the 6620) under the column has to move more oil to steer. They should not feel "heavy" unless you are used to something that steers real light like your TRUCK.
The hydraulic pump under the seat does have a separate section just for the steering. (I think the unloading auger swing shares the circuit too.) The steering system shares the reservoir with the main pump but has its own separate pump section. You can check the pressure on the steering circuit. There is a test port on the side of the hydraulic pump. You dead head the steering and the pressure will spike to what the relief valve is set to.
I would either have some one that know what they are doing check it out or buy a JD service manual so you can check it out.
The hydraulic pump is different on the heavy rear axle machines. The pump has higher flow for the double steering cylinders. I have seen the wrong main pump on the heavy axle and it will make them steer funny.
The steering control "pump" is different on the double cylinder axles too. So you may have the wrong one of them on too. The correct one, for a double cylinder axle, is part # AH142441 list $1393.85.
I would have some one that is "used to" a JD Titian II drive your combine. You may have nothing wrong other than you are used to the Gleaner "K".