Actually, we support pushing data as well! We have a few users with a similar use case, who push journal entries and invoices from their apps to Quickbooks/Sage/Xero, etc.
We have pretty good coverage on Quickbooks, but if there's something specific you'd want to push or pull that we don't support already, it can be added pretty easily.
As mentioned in our post, all of our connectors are open source and built on Python, so our engineers regularly add support for new endpoints as users request them.