Are there any alternatives to meditation in regards to property distribution other than agreement or trial? Why can’t the 2 attorneys involved negotiate a settlement without the extravagant expense of a mediator?

*Not an Attorney
That is what we did in our case. The attorneys hammered it out and we submitted a Consent Order to the court for separation and ED. Don’t know if it will work for you but I know it’s possible.
Hope it helps.

Yes, you can just mediate it at one time between the attorneys instead. The four of you will meet on the appointed day and will try to settle everything possible. This is referred to as a settlement conference. However, this is only likely to work if both sides are willing to negotiate. A good mediator can faciliate a settlement better in trickier cases and will work with both sides to compromise.