A330
Surely, to get the full-flavour experience of BD, you have to go to one of the 330 destinations?
ALA, ATQ, FNA, RUH, DMM, JED
So, three ruled out due to visa restrictions, one ruled out due to insecurity (calibrate your own sense of danger), which leaves ALA and ATQ.
If you get extra special lucky, you too could end up being delayed by the engines on WWBD going tech - again.