Alien technology would be a good way to explain time travel. Or some invention of Professor Pearl's that goes wrong.
That too, though originally I was trying to figure out why Dr. Rough doesn't forget Dream. Maybe Melissa's father is a failed inventor. He created the time machine which doesn't function properly when they try to use it to eliminate 00Carter, and sends everyone into the past instead of just Dream. Sexi eventually gets abandoned in the past, doomed to relive everything.
I missed trying to tie crazy ideas together LOL.
Okay so Dream attack HimTak, maybe they're a girl group from a past mission of Nick's, Melissa of course being Nick's way in who got forgotten once the mission was over. She thought she'd get a relationship and got nothing. They have hated him ever since and want to bring down Nick by erasing him from existance. So Melissa gets the technology from her failed father. And it sends everyone back in time. Perhaps Howie and Sexi were meeting with Drums (who has updates from Styx) outside of Vegas (how ironic Nick lives here now since HimTak is based in NV lol) when the whole city gets thrown back in time. They also got the wrong year. They aimed for 1980 and got 2006. Eventually they're defeated back Howie helps bring them back into the present, being a proper genius though it costs him Sexi for some reason. Everyone has forgotten them now except for Howie/Drums and he tells them to come join him as he'll one day make sure everyone knows their name once more.