My beagle insists on 'helping' with laundry but ends up dragging socks everywhere

I recently started doing laundry in a room where my beagle, Max, can hang out. At first, I thought it was cute how he’d sit by the basket, watching me sort clothes. But now, he’s taken it upon himself to 'help' by grabbing socks and dragging them all over the house. I've tried distracting him with toys and giving him treats when he stays away from the laundry, but the sock chaos continues. I’m worried he might swallow something or ruin my favorite socks, and it’s starting to feel like laundry day is a battle zone. Max is about 3 years old, pretty energetic but well-trained otherwise. I’ve considered shutting him out of the laundry room but worry about making him feel isolated. Has anyone else dealt with a dog who’s obsessed with laundry? How did you keep your pup entertained or redirected without shutting them out completely? Would giving him a special 'laundry day' toy or treat work, or should I just keep the door closed?