Hi Oliver.
I think it depends on your budget. If you can afford to invest in a headless platform then am sure you can get it to work. We are looking at having three cloned Shopify Stores (one for UK, EU and US) and each will have their own integration with their own third party warehouse. Not ideal, or straightforward, but seems like the best and most affordable solution at this stage. We are using https://www.coderapper.com/ for this work, so feel free to reach out to them.
Thanks
Dan