Hole saws are not precision tools. Theyre meant for construction, to put a mostly properly sized hole in something. Some runout on the saw is to be expected, and the larger diameter will magnify any runout present in your drill press (and unless youre using a milling machine, i can pretty much guarantee you have a decent bit of runout in the machine). If you want a clean cut, hole saw just isnt the best thing to try. A circle cutter like this would be a much better bet:
https://www.amazon.com/General-Tools-55-Cutter-Adjustable/dp/B00004T7P1
Make sure the cutting bit is dead sharp, clamp the stock down firmly, and most importantly you need some way to keep the plug in place as well. Use some double-sided tape to stick the stock to be cut to a backer board, then just barely cut into the backer. The tape should keep the plug from turning into a projectile when the cutter breaks through the stock