I am not sure I am following you.In my experience,"barrel wrench"may not be the right term.The barrel does not turn in the upper receiver.There is a barrel nut that tightens to the upper receiver,over the barrel extension.There are barrel nut wrenches.I have used the GI pattern,the DPMS pattern,and the
Yankee Hill pattern.All of them have 3 dowel pins that engage the holes through the barrel nut that the gas tube passes through.None of the tools I used would have any problem with a bull barrel.Now some how you have to hold the barrel or receiver while you torque.
I have used the aluminum vise jaws that fit various barrels,and I have a splined wrench(Brownells) that goes through the upper and engages the locking lug recesses.Some use the ones that clamshell around the receiver.
You might consider a GI armorers tech manual,or some of the other references available to step you through it.