The UK APD is not a luxury tax per se. In any case, it's only charged on departures from the UK, and the rate varies heavily by distance. Thus, something like MPS-LHR(stop)-AMS-PRG//BUD-CDG-JFK-MSP would only incur the short-haul UK APD, which is £26 from next month (half that for economy, so if money's tight, take the intra-European flights in Y). The UK to US APD, on the other hand, is £130 (half that for economy). You could also do MSP-LHR(stop)-AMS/CDG(stay for over 24 hours)-MSP and pay the lower rate of APD.