But while Jon wasn't able to say it with flowers, the former couple were able to express themselves well in other ways, leading to a "successful and productive" session, his lawyer Mark Heller tells PEOPLE.
"This has been called the real-life War of the Roses," says Heller, referring to the 1989 black comedy in which Michael Douglas and Kathleen Turner played bitterly battling spouses, "and he brought that as a peace offering to break the ice and try to bring the war to an end."
Things went so well for the Jon & Kate Plus 8 stars that the arbitration's scheduled second day, planned for Monday, is no longer necessary. The arbitrator is expected to rule in a month, and Heller says "it's possible" the contentious divorce could be finalized by the end of the year.
"It was a positive move in the right direction for us to bring them together to the mediation table," says Heller of getting Jon and Kate into the same room for the hearing. "Obviously before two warring parties can smoke the peace pipe, they have to sit down at a table and address the issues that brought them to the skirmish."
On the table: discussions of everything from custody, child support and distribution of assets. "There were a couple of very emotional moments, " says Heller, "but in the end it all came together and concluded on a happy note."
Jon was "very relieved," adds Heller. Kate, meanwhile, left the courthouse without commenting, and her attorney declined comment to PEOPLE.