Always looking for new ways to do things, I tried the pulley puller and I prefer the press.
I use two pieces of flat stock to help support the trunnion in the receiver stub. Make a V with the flat stock with the barrel at the base of the V and the tips of the V at the top of the receiver. Place a penny over the chamber and I use a piece of 5/8 steel rod to press the barrel out. I don't mark anything. The allowable space between the rear sight base and the front trunnion will only allow it to be out of alignment by a hair, and if it is out of alignment, you will know it when you put the barrel pin back in. Total time pressing a barrel out with time for set-up is about 3 min. I can't even get the puller on the trunnion in that time.
Oh yeah, it makes it alot easier if the barrel pin is out.... and I have tried it both ways, not often but I will admit that I have been rushed before.