First off, just to clarify, does that "TR" stand for tons of refrigeration?
The "rules of thumb" equations I posted before mean that the gpm required for the condenser is "typically" about 1.25 times more than that required for the evaporator. This number, similar to your 1.17, is presumably a ratio of condenser to evaporator heat rate. The actual factor will depend on the specific refrigerant, operating refrigerant condensing and evaportating temperatures, subcooling and superheat degrees, and compressor efficiency.
Assuming your 1.17 is the real number for your specific application, I would think the gpm for condenser water cooling would just be 1.17 times the gpm you get for chilled water flow rate.
In your example, if you're using the "rules of thumb" approach, you wouldn't multiply the tonnage by 1.17 and then use the 3 gpm/ton rule of thumb because that would be like multiplying by 1.17 and again by 1.25 or effectively multiplying by 1.46. If you want to use the 3 gpm/ton as an estimation, do it based on the 600 tons which would make your cooling tower flow rate 1800 gpm (@ 10 deg F), not 2106 gpm.
On the chilled water side, if you know you have a temp difference of 16 deg F, the flow rate would be (600 x 24)/16 = 900 gpm.
I assume your driving at "can we now take the 900 gpm and multiply by 1.25 to get 1125 gpm (or 1.17 to get 1053 gpm) condenser water flow (vs. the 1800 gpm)?" I don't think you can reduce your condenser water flow rate accordingly just because the chilled water flow rate is light (i.e, high delta T), because from a practical perspective, you won't be able to get a 16 deg F delta T at the cooling tower. Maybe someone else can weigh in on this last part...
