I have used both carlson and trulock extended and flush chokes. I have patterned both and they both pattern about the same given the constriction. I find the finish tends to be slights better on the trulocks, so I prefer them. However, I buy the one that happens to be on sale.
That included wrench is a cheap novelty item that might work in a pinch. Purchase a higher quality choke wrench that grabs all 4 slots.