OAKLAND — If there were any lingering doubts over whether BART’s bitter labor dispute will be settled soon, they were eliminated Wednesday when the rail line said the opposing sides were staring down a nearly $100 million disagreement despite months of talking.

During an extraordinary airing of grievances, management and unions testified before a state panel commissioned by Gov. Jerry Brown to determine whether he should, by Sunday, order a 60-day “cooling-off” period to keep trains running at least through mid-October.

The hearing finally provided some clarity on where each side stands after all the public posturing. But there was no less acrimony.

BART calculated that its proposal for employee pay and benefits would cost the agency $99.3 million less over four years, compared with the unions’ current offer. Union leaders rejected that figure, but their own calculations put the two sides $56 million apart over three years.

Panel members, at times acting like parents to two feuding siblings, repeatedly reminded both sides that they were not there to determine which side was right but to simply figure out whether another strike would be likely without Brown issuing the two-month delay. The panel’s public report, expected Friday, is a legally required step before Brown can issue the longer strike ban.

Union leaders urged Brown not to call a two-month truce, saying that if only management would have a “change of heart” and offer employees more money, they were confident they could reach a deal by Sunday night’s deadline to avert a second strike Monday.

“I can see an agreement — and I would not say that if I didn’t think it was possible,” said Josie Mooney, chief negotiator for the local Service Employees International Union, who maintained that management was stalling.

BART executives strongly disagreed, saying they weren’t about to cave now after three months of negotiations and needed extra time at the bargaining table to avert an even lengthier rail shutdown.

At least one panel member saw the agency’s point.

“I’m daunted by the number of proposals,” board member Micki Callahan, San Francisco’s human resources director, told union leaders. “I’m a little surprised to hear you think this can be achieved by Sunday night.”

Both sides announced that they would return to the bargaining table Thursday and Friday for the first time since Brown averted a second strike last weekend, but during the public hearing, they spent hour after hour bashing one another yet again.

The hearing provided the first publicly released proposals since state mediators issued a gag order on the talks following the end of the first, 4½-day rail shutdown on July 5, but they appeared similar to the offers released more than a month ago.

BART’s total four-year proposal would cost the agency another $18.5 million while the union’s offer would cost $117.8 million over the same time, BART’s budget staff estimates.

Management’s offer includes 9 percent wage hikes and a 5 percent increase in employee pension contributions for current workers, both slight concessions from a month ago, while new employees would pay a slightly higher share toward pensions. Blue-collar union workers currently do not contribute toward their pensions and earn $76,500 in gross pay on average.

According to BART, the rail line’s two largest unions countered with a three-year deal totaling 21.5 percent in pay bumps, including an 11.5 percent increase in the first year. The unions, however, insist that the raise is actually only 15 percent over three years because 6.5 percent of their total pay raise would be offset by larger pension contributions.

Vincent Harrington, an attorney representing the local Service Employees International Union, said their pay increase proposal was about equal to the same amount of real and predicted inflation from 2008 to 2016, since employees’ wages have remained flat for several years.

“As we run to catch up over the wage freeze,” Harrington said, “we’d like to at least be running in place, and not running behind.”

The final of the three main issues — health care — represents a much smaller dispute, however. Employees currently pay $92 each month for medical benefits, or 5 percent of the cost, and management has dropped its offer to double that contribution to 10 percent, leaving the sides just $4.3 million apart, BART estimates.

“Unfortunately, we remain far apart on the major issues of this contract,” General Manager Grace Crunican said.

Dozens of employees clad in purple union shirts reading “will strike if provoked” packed a state office auditorium in preparation of the hearing, which was chaired by Brown adviser Jacob Applesmith and also included former construction union president Robert Balgenorth.

Tensions ran high when the panel opened the floor for public comment, with some audience members booing speakers who criticized BART employee salaries and applauding those who spoke out in support of workers.

One of the last audience members to speak, a station agent and union negotiator, grew teary-eyed as she spoke about her desire to negotiate with management.

“I don’t know why there’s so much disdain from our employers,” said Yuri Holley. “I implore you to please help resolve this because I would like to get back home and resume my duties as a mom, a working mom.”

Staff writer Brittny Mejia contributed to this report. Contact Mike Rosenberg at 408-920-5705. Follow him at twitter.com/RosenbergMerc.