Would openings cut into supply ducts improve cooling on the warm side of my house?

Would openings cut into supply ducts improve cooling on the warm side of my house? Ranch home, finished basement not a walkout. The basement floor is radiant heated and there is no AC vent to the basement. The stairway is unobstructed. There have been complaints of "stuffy" and "not cool enough" during the summer. There are seven equally spaced 6" cylinder ducts over the North 1,000 sf of this 1,500 sf space. That's the targeted space. The South side has three ducts. Each duct runs about 20 ft from a central trunk. My thought is a couple of 2-3 inch cutouts tapped into the overhead supply lines that feed the main floor would cool the basement. Is this a good way, or is there a better way?