Despite being separated for more than a year, Demi Moore and Ashton Kutcher are still locked in a fierce private battle over the financial terms of their divorce settlement.

Sources tell us that lawyers for Kutcher, the highest-paid TV actor last year, and Moore “are trying to negotiate a settlement out of court and out of the public eye.” But “they still haven’t reached an agreement over money, because Ashton earned substantially more during the final years of their marriage, but he doesn’t want to pay a large settlement.”

And one source added that if they don’t reach a private agreement, “the discussion could boil over into a public court battle.”

PHOTOS: DEMI MOORE

Kutcher, who made $24 million last year, and Moore split up after six years of marriage when he was reportedly caught cheating during their anniversary weekend. He has since moved on with a very public romance with former “That ’70s Show” co-star Mila Kunis.

Meanwhile, Moore has been putting on a brave face in New York the past few days, hosting the GEMS Gala Wednesday before heading out to dinner with friends.

Thursday night, Moore attended a birthday party in Red Hook, Brooklyn, for Kabbalah leader Karen Berg, whose son Rabbi Yehuda Berg performed the marriage ceremony for Moore and Kutcher. Sources tell us the bash, which was catered by kosher powerhouse BB Prime Butcher Baker, had a Texas-hoedown theme with hay bales and fire pits and a family-style dinner at long tables.

Witnesses said Moore turned up in jeans and boots with three girlfriends and “looked happy and mingled with other guests,” including Donna Karan, Cobra Starship’s Gabe Saporta and the Berg family. Notably missing was Madonna, who’s touring, and Kabbalah co-founder Philip Berg, Karen’s husband, who has suffered health problems.

Guests enjoyed Romanian skirt steak, short ribs, sliders and other Southwestern favorites. Demi, who ate short ribs and corn, sat with her friends in the garden before coming in to dance with Karen. Her rep didn’t get back to us.