During the recent past, passenger air transport has been recovering from its significant retraction during the Covid-19 pandemic. If the recent significant drop in air traffic due to the pandemic acted as an external mitigating factor to airport traffic congestion in several major airports around the world, with the post-pandemic air traffic recovery airport capacity is likely to, once again, fall short of demand and not keep pace with the growth in air traffic. For this reason, close to two hundred major airports worldwide, most of them in Europe, face capacity constraints. Eurocontrol predicts Europe's capacity shortage in 2050 at 500,000 flights/year given the baseline scenario, which could rise to 2.7 million based on an optimistic scenario. The allocation of airport slots in Europe and elsewhere is still ruled by administrative processes, based on IATA's Guidelines, which follow historical precedence and time adjustments of historical slots. Market mechanisms in slot allocation, as an alternative to administrative processes, are controversial and still rarely used. Several authors have highlighted the inefficiency of the current airport slot administrative allocation system, based on those guidelines. Some have suggested improvements within this administrative system, others have suggested new mechanisms altogether, such as congestion pricing mechanisms and other market mechanisms involving auction procedures. Among the various auction mechanisms, scoring auctions and the Progressive Adaptive User Selection Environment (PAUSE) methodology have been suggested. In this paper, and following our previous work, we explore and extend the application of the PAUSE auction mechanism with bidding based on a score function for the auctioneer, which includes another variable in addition to total revenue, where this variable represents the quality of the service provided. We suggest the application of this auction mechanism, in a gradual fashion, to the three international airports operating in Portugal that are level 3 all year round. The different airlines using these airports would still follow the current IATA guidelines during their use of other airports, including the slot exchange protocols. We suggest that some of the PAUSE auction mechanism's desirable properties, such as computability, transparency, absence of envy, and the mitigation of the "price-jump problem", "threshold problem", "exposure problem", and "winner's curse problem", still hold.