Yep, encountering this issue too. Spoke to Shopify Support but they only provide support for the API via the forums. However, they did suggest that, because you cannot actually edit order dates from the Shopify admin, it is unlikely you can do so via the API.
Problem is, if you cannot edit the order date to match the order you are importing, the value of importing orders is pretty much void. Arguably you could put the original order date in a meta field or the notes, but this is of no use for reporting purposes.
Would be good to try and encourage this addition to the API - but there may be a security issue that we are not aware of?