The trio were in the field chasing three wildcard spots for the 2026 LIV Golf season.
But those went to winner Richard T. Lee of Canada, Bjorn Hellgren of Sweden and former wunderkind Anthony Kim on Sunday.
Lee sailed to a five-shot victory by following Saturday's 64 with a 65 to land at 11-under 129. Hellgren shot a 64 to finish second, one shot head of American Kim (69).
Jones, Crawford and Wood finished in a six-way tie for eighth at two under to sneak into the top-10 plus ties who received Asian Tour International Series exemptions.
Two-time PGA Tour winner and two-time Australian Open champion Jones, 45, played the LIV Golf circuit since signing in 2022, featuring on the all-Australian Ripper GC team, but struggled in 2025 and lost his spot.
Young gun Elvis Smylie is reported to be set to take up the vacant berth in the Cameron Smith-led Ripper team.
The biggest name at the LIV Golf Promotions was Kim, who retired from golf for about 12 years before signing with LIV in 2024 for his comeback.
A wild card for two years, Kim was relegated after the 2025 season.
After he made the cut on the number on Friday at Black Diamond Ranch, the scores reset and Kim went 66-69 on the weekend to place third at five under par.
It marks an eye-catching turnaround for the 40-year-old from California. Kim also went through rehab for drug and alcohol addiction and has said before that doctors had given him grave warnings about his health.
"There's a ton of satisfaction. A ton," Kim said. "I'm sure I'll understand that all that work has really shown this week, maybe later tonight when I'm drinking an iced tea.
"But yeah, it means a lot to me because three years ago, doctors had told me that I potentially had two weeks to live. So just to be here standing in front of you guys is a blessing."
Lee was the best golfer all week. He shot a 64 Thursday in the opening "play-in round," which Hellgren, Kim and others were exempted from.
He's now the first Canadian player to become a member of LIV Golf.
"I think more Canadians should come in and we should make a team," Lee said.
The others to receive Asian Tour's International Series exemptions were Denmark's Lucas Bjerregaard, South Korea's Jeunghun Wang, Thailand's Sarit Suwannarut, Zimbabwe's Kieran Vincent, South Africa's Oliver Bekker, Thailand's Jazz Janewattananond and Japan's Takanori Konishi.
