Unable to ship due to stock limits

Hello,
I hope you might be able to help me with this.
When ordering new inventory- the shipment takes 6 weeks to get from the warehouse in China to the UK Amazon fulfillment center by sea.
Long story short, with this lead time I will need to get the shipment sent in the next couple of days or I will almost certainly run out of stock by the time it arrives.
The issue is, that with the current limits on stock levels I am unable to create a new shipment with the inventory levels as they are.
I have contacted Customer support but am unable to get any valid advice, it seems I am just getting automated responses about how to check my inventory levels and other irrelevant and unhelpful info. It appears that Amazon takes no consideration for how long the inventory will take to reach them, and I can’t seem to get anyone from the help centre to give me a straight answer.
What I need to do is to find a way that the stock currently in a warehouse in China can begin the long import process while the current stock in Amazon FBA sells out.
Have any of you experienced this before, or do you have any advice for me? The only alternative I can think of is to have the shipment sent to my house but as the order was DDP, this will incur additional unnecessary costs.
Thanks in advance, I really do appreciate your help!