As it isn't currently airworthy it doesn't need an export C of A - its just a heap of spare parts - some of which are time-ex, most of which are not - all bolted together in the shape of a "ship". (shipshape?) What happens if you ship it out with all the log books and documents but without the export C of A, do the overhaul at the other end and then apply to register it? One supposes that all would depend upon the attitude of the other airworthiness authority - though unfortunately it isn't just the CAA who are stupid.
Kit planes can certainly be built by anybody, but every step must be certified by a PFA inspector. Then the complete heap is inspected again before being test flown by a pilot experienced on type. Not exactly "no skills cobble it together and fly.." is it? After all that inspecting and test flying it still doesn't get a C of A - it gets a 'Permit to Fly'.
Orville and Wilbur had it easy...
...until they tried to build the Mk II...