Tapping a 7/16" X 20 TPI thread into 1/2" mild steel

Am I going to have to buy a tapping head for my drill press?

What do you think of "chip-free thread forming" taps? McMaster-Carr and Grainger are pretty proud of them.

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No. This is used on aluminum or other soft metals.
Since your holes go all the way thru all you need is a hand taper tap ("starter tap") and just run it all the way down, making sure you have full threads all the way. You don't need any fancy spiral taps, those are for production work where you need to get the chips to come out (usually on blind holes). Just lube it up good with your choice of oil or grease and take it about 1/2 turn at a time, backing off a little each time.