That Park locknut wrench is absolute garbage, it doesn't even come close to fitting tightly on the nut. Several way better alternatives have been made by J.A.Stein, Trek/Wrench force and probably others.

The smaller of the two Wrench force locknut wrenches made: Wrench Force 30mm 32mm Professional Headset Wrench by Snap-On New! Heavy Duty!! | eBay

The 12" Knippex smooth jaw plier wrench is also a popular choice, designed to not damage soft/nice/chrome plumbing fittings. A little pricey though.