Whilst an upright position would be preferred, I am struggling to imagine how the box would stay upright (it is now ~80cm high, but 20cm wide).
Where is the 14 day notice thing stated? As far as I am concerned, I am carrying a box of luggage, not a bike (for the purposes of national express).
Bike is now boxed up and I have booked the coach ticket, funfare,with no flexibility to shift to later coach, nor any extra luggage fee (it looked kind of useless paying that supplement in advance since it says I can pay on the day too). I have a later train as an insurance policy, though that is also not 100% certain it will be allowed, otherwise I would have gone with that. Put together I think the chance of success by bus or train exceeds 99%, although individually they are perhaps 90% bets, if you get my drift.
Will let you know how it pans out, not travelling till May.
I think long haul flights are a bit different to European flights eg I doubt I would risk taking a "ctc plastic bag" on a long haul flight (though it depends on the airline and the airport).