Two-way data sync over REST

We have just started using SpiraTest and we're trying to reduce any barriers to adoption by automating as much of the workflow as possible.

One of our development suppliers uses their own work-tracking tool that assigns work to developers, but also holds all the requirements and defects. We have asked them to use the SpiraTest REST API to create Releases and Requirements in SpiraTest when they are baselined in their development tool, but I would also like defects to be kept in sync between the two systems as they are progressed.

We have a custom defect workflow that mirrors the developers system:

https://www.dropbox.com/s/ligj7bug9000a32/New%20Defect%20Lifecycle%20%28with%20Dev%20Tools%29.jpg?dl=0

In this workflow half of the time the developers system will be updating SpiraTest over REST - which we can implement now. The over half of the time we need to update their system. Has anyone managed to get something like this working?

Many thanks,

Dom.