I don't think this is a matter of being cheap, it looks like a matter of inexperience in the SAR world. The CivSAR machine in question appears to have had both the staff and the equipment to operate as you suggest, but it looks like the operator lacked the experience to put those tools to good use, and the crew were not adequately prepared to deal with their input.
Punto - the problem is that even with well trained ex-mil radar operators, the civil system won't allow those without flight crew licences to be responsible for the navigation of the aircraft.
So, even if the rear crew are trained to use the radar ( and they do have the screens in the cabin to do so) they can't 'control' the aircraft in the same way as a mil Radop would have done in the Sea King.
Personally I see this as a retrograde step that pushes workload to the front of the aircraft in poor weather or at night when it could be managed much better using more of the crew.
Perhaps it is something that could be addressed through the AOC to give derogations from the 'normal rules'.
However, I wouldn't be surprised to find that some CivSAR crews do operate the 'old-fashioned' way because they have ex-mil Radops with a great deal of skill and knowledge in manipulating the radar.