Baddeley had six birdies in a bogey-free round in shifting wind conditions at Montreux Golf and Country Club, scoring 12 points under the format that awards eight points for albatross, five for eagle, two for birdie and zero for par, and subtracts a point for bogey and three for double-bogey or worse.
"It's a tough day today," Baddeley said. "The wind was really gusting and gusting in different directions. You really had to wait until it was your turn to hit, pick a club. Because it could be 15 downwind, switch and be 15 straight in to you. It was just crazy."
Baddeley had a 26-point total for a one-point lead over Schniederjans.
"My game's been pretty good," Baddeley said. "I haven't capitalized with the putter and just been working really hard on that. Been hitting the ball pretty solid this week. I'm hitting the ball well and making a few extra putts, which has been nice."
The 37-year-old Australian won the last of his four PGA Tour titles in 2016.
Schniederjans, the first-round leader, fell back with the double-bogey in the tricky wind on the par-3 seventh -- his 16th hole of the day.
"It's frustrating," Schniederjans said. "But everyone else who is out there this afternoon is dealing with it. Cost me big time on 7. I hit it and it went straight down to the left."
Saunders, Arnold Palmer's grandson, had a 13-point day with seven birdies and a bogey.
"It was a good solid day out there," Saunders said. "Drove the ball really well and made a few more putts today than I did yesterday. Still left a few out there. But it's a fun format and enjoy giving myself as many birdie chances as possible."
Putnam scored 17 points, 11 on his last seven holes with an eagle on the par-5 13th and four birdies. He hit a 213-yard approach to a yard to set up the eagle.
"Shot, I think, 30," Putnam said. "That eagle was big."
Merrick had a 12-point round.
"I hit a great little wedge shot, landed short of the pin, shot pass and spun," Swafford said. "I told it to disappear and it disappeared. Five points is definitely nice in this format."
The winner will earn a spot in the PGA Championship next week at Bellerive, if not already eligible.