I used the same type tool and it worked fine. I didn't have to disassemble the actual hooks, just unthreaded the hook assemblies and put them inside the spring and then thread the rod through. Was not fun, but worked fine. And felt safe with the hooks grabbing the springs on both sides. Also Be sure to seat the springs properly in the "slots" when putting them back in.

The tool I used was from NAPA Pt#3450 Coil Spring Compressor