If you were to make this antenna, and then use a 4:1 transformer/balun, it would basically transform 50 ohms down to 12.5 ohms - something far worse than a small 50-75 ohm mismatch.
So a direct-connection to your 75 ohm cable is better. Are you perhaps thinking of a "current balun" that only suppresses common-mode shield current? If so, here a direct-connection is used, but perhaps a few snap-on chokes near the feedpoint is all you need - no impedance transformation necessary.
You could try using your 1/2 inch tubing, BUT I can almost guarantee that it won't perform as expected unless you change spacing, change element lengths etc that are designed for a larger conductor than what is shown in the article. Instead of a high-gain unidirectional yagi, you end up in the real world with a low-gain bidirectional antenna or something odd since it wasn't designed up front for 1/2" tubing.
I don't know what your mounting / environment is, but if it isn't too bad, you could even use straight #12 copper wire if that is more convenient, say up in an attic or other shielded area.
A 4:1 transformer here will do more harm than good. And it isn't in the article either.