Containerising an aircraft in Arizona and shipping it to Hungary certainly wouldn't leave much time out of 6 weeks for even a large team to conduct a rebuild. I'd guess you'd not have the shipment delivered in less than 2 weeks and that would be miraculously fast. You'd then need almost instant access to all the other components you needed, plus time to rig, paint and flight-test it. Not to mention the hordes of engineers to do the work.
Anyone in the freight forwarding business know how long these things take? I can't imagine you'd get it boxed and trucked to a US dockside in less than 4-5 days. Then you've got to find a ship ready to go to a suitable European port, then clear customs and truck it to Hungary. Quite a trip.
I suppose if EG has a stable full of Stearmen they could have been used as Christmas Trees but even so, quite a feat. I can think of a quicker way but it wouldn't be fair to suggest it without a shred of evidence.
On the motives for having EG on board so much of the time I wouldn't be surprised if the Caravan was so overloaded, even by African standards, that they pretty much had to "lose" someone into the Stearman. A Grand Caravan has a theoretical payload of about 1500Kg. 5 pob with bags = 500Kg. Four hours of fuel plus a reserve = 500Kg. And the remaining 500Kg won't go far at all with film gear, let alone spares for both aircraft, oil for the Stearman (and that extra fuel they wanted to tanker sometimes. Heaven knows how they ever did that.
btw, why did TCT quit flying at Old Warden? Are we missing something?