Last time I had to hold a water pump pulley I bought a truck oil filter wrench removed the rivet put it around the pullley and place a bolt in it I put a small thin rubber strip to keep it from slipping its my version of and overbuilt strap wrench. I got the fan clutch off without issue and I now have a dedicated tool for sizes X-Y.
You could also try a proper strap wrench but dip the strap in some sort of rubber coating to increase the grip. The rigid and other pro style tools are nothing like the craftmsn of HF rubber style strap wrenches...
That was before I got my pneumatic fan clutch set.