Posting Partial and Third Party Payments

We're a new venue, starting our third season so new things are coming up. One is a gala with another non-profit.  I'm wondering how others handle partial payments? 

For example, someone purchases a $3,000 ticket.  They have a donor advised fund with the other organization and send us the $400 by personal check (non-deductible) and have the other organization issue a check to us for the $2,600. 

I book money as it arrives. I'm not seeing how this comes out in reporting. Tess doesn't list unpaid tickets, and the Single Sale Order Listing report shows what's due but doesn't help when sending daily batches to finance.

How do you handle reporting of partial payments to your finance departments and/or booking payments made to another organization (third party payments)?

Thank you in advance for any wisdom!