that is some thick stuff. can you post details on your machine and cut speeds etc. I notice bevel on certain directional cuts. So say its going around a corner and coming back one way the flame is behind and or bent and creates more bevel. You could try cutting slower than hyp suggests. Clean air obviously helps and what pressure is at the machine? Lot of variables to tackle and I know it can be frustrating. I took my torch off and checked the Z axis and it wasn’t sq, so that helped me alot too. Hard to really tell if its sq with just the torch on there. I highly doubt that swirl ring will help, those last for a loooong time. new consumables are def going to be helpful on that stuff. I use copper plus electrodes. I cut alot of 1/8, 3/16 and 1/4 every week. Last set I took out I was able to get 4500 pierces and tons of inches of cut. I normally get around 3k pierces bf I put new consumables in.
FYI the pierce delay in Hyp book vs what the PRO will want is a little off. I add about .3 sec or so in my program. If you get a short pierce and say too much cut speed that flame isn’t going to have a good chance of staying straight. So add alot more pierce if need and really slow it down. Then you can bump it up manually in the FC to find the sweetspot.