I would not add holes to Charles burners. However, the position of things is important.
First, lets talk about the burner mount:
The burner port tube is the pipe sticking out the forge to mount the burner. It should be about 3" long. Too short or too long may affect the burner operation, especially on smaller venturi burners. The tube ID should be about 150% the size of the burner OD. This space allows additional air to be drawn by the flame as it enters the chamber, as well as allows some cooling space around the burner. In a 2BF, the opening needs the same extra space. Never make the burner port a snug fit to the burner.
I recommend two sets of retainer bolts instead of one set ( the three bolts at 120° spacing that hold the burner in place). This assures the burner is straight down the port tube and has an even space around it to draw extra air ( and stay cooler).
Lets talk venturi:
The gas ejects from the orifice at a high speed. This pulls air molecules along with it by creating low pressure around the jet. This is the "draw" of the burner. The position of the jet, and the amount of space around it are important to get the right draw. Charles had been working on a sliding choke to move up and down the burner tube to adjust the draw. That is how you tune a venturi burner. Charles has worked out the orifice size and position of the jet pretty well, but a sliding choke may help a lot. You can make one from a piece of thin sheet metal. It doesn't need to move much to change the burn.
Now, the flame entry point:
Next, the flame needs the right path to enter the chamber without creating turbulence. Besides the right size port tube, the size and shape of the entry port matters. Normally, the end of the burner tube is about 1/2" to 1" back from the chamber wall. Additionally, the shape of the entrance hole changes things. A straight hole through the refractory (or just the burner sitting flush) will cause turbulence. Bits of loose refractory wool, and jagged refractory will make it worse. A smooth bell shaped entry ( called a flare) is better. I shape the hole in the wool to flare out and use satanite to make it smooth and have a nice bell shape. Some folks make a wooden or wax bell shape and use it as a forming mandrel as the refractory dries. Some folks put a slight flare on the end of the burner tube, which can help, too. You can either forge in the flare on a tapered mandrel, or use a slip-on flare. HTT&R sells these flares.
By moving the burner in and out in the burner port tube ... and keeping it centered ... you get the best position for smooth running. Adjusting the choke (if you have one) can tune the flame for a neutral atmosphere. It take some trial and error, and you have to go back and forth between the things that change the flame to get the perfect balance. Now, on word of caution - do all adjustments on a fully heated forge. Let it run 5-15 minutes before you make any fine adjustments. If you do it cold, you can pretty much guarantee that it will burn different when the chamber is heat soaked.