Hi,
I have done similar project that mapping 2 services vend and sm8 (invoicing services in Australia).
Your project is tougher because Bexio & Unleashed has no mechanism to notify in real-time when new contact/product/ invoice created/updated.
So the solution for it is we should poll api each 5s, so we can know if new product added on Unleashed, we will push that product to Bexio.
With above solution, we resolved the scenario: end user does action on Bexio/Unleashed website via their account, then our service will automatically check the change and sync to other platform.
Beside that, I have another suggestion, we will build a website that user will login to use, then they can post contact, product, invoice via our website, then those items will be posted to both Brexio and Unleashed via api.
Mean by this way we have central place for user to work, of course we have some limitations such as /Invoice api is not ready for Unleashed, so we can go with polling for Invoice, then once api is ready, we switch to use api.
Let me know if you're interested in my suggestion.
Thanks,
Duy