The development of the considerable transport and logistics potential of the Kaliningrad region is hampered by several factors. This problem, to which we will refer to as a transport deadlock effect, translates into the limited contribution of transport to the regional economy. Particularly, it manifests itself at the level of regional gross value added, where the contribution of transport is much smaller than one might expect given the significant role the industry plays in the economy of the region. In this study, we examine major ways of increasing the economic efficiency of the regional transport system from the value added perspective. We posit that the structure of cargo handled and the redistribution of value added in favour of regional actors have the dominant influence on economic efficiency. Using our own simulation model and the earlier developed system of transport tariffs and value added calculation for the Kaliningrad region, we produce scenarios and consider changes in value added in the case of selected cargoes carrying intermediate, investment, and consumer goods (as defined in the International Classification for Broad Economic Categories ICT BEC-4). Our calculations show that higher value added and greater economic efficiency of a regional transport system are associated with re-orientation towards investment and consumer goods. The most visible effect is associated with rail and road transport. As to sea transport, the decisive role is played by an increase in the physical volume of cargo handled. The results of this study and its modelling tools can be applied in the analysis of the current situation and in the assessment of the efficiency of transport systems in other regions. Another possible application is the identification of growth conditions for an industry, particularly, when developing projects and proposals for increasing the efficiency of transport services.