Space division multiplexing (SDM) is a promising approach to overcome the looming fiber capacity crunch. Joint and fractional joint switching (JoS and FJoS) architectures, which switch multiple spatial dimensions together as atomic units, have been proposed to reduce the cost of implementing SDM and cater to strongly coupled transmission media. However, they have been shown to impose significant penalties to overall network performance, at least when many relatively small connections are used in the context of uncoupled spatial dimensions, while performing nearly as well as the independent switching (InS) architecture if the average connection size is sufficiently large to efficiently exploit their increased granularity. In this work we tackle the performance penalty that JoS and FJoS architectures impose on SDM networks with uncoupled spatial dimensions compared to InS, by proposing two novel routing, space, and spectrum allocation (RSSA) heuristics that effectively share jointly switched resources, adapted to use different types of SDM reconfigurable optical add/drop multiplexer architectures requiring only a small additional cost. We investigate the performance of these new RSSA algorithms compared to an existing one under several traffic conditions and models using simulations. We find that our proposals can achieve significant improvements in the performance of SDM networks carrying large numbers of relatively small connections, up to parity of performance with InS designs, at a lower implementation cost, under all traffic conditions under study, including different average connection sizes and size diversity.