We propose a novel receiver architecture that preserves the performance benefits of multiport selection in fluid-antenna systems while requiring only a very small number of radio-frequency (RF) chains. The resulting fluid-antenna hybrid multiport (FAHM) receiver effectively decouples port selection from signal combining by integrating a low-complexity analog combining network similar to those used in conventional hybrid multiantenna designs. We develop a stopping criterion to determine the number of selected ports, which limits the performance loss associated with port selection, and then design the hybrid combiner for a given RF-chain budget. The FAHM architecture is evaluated in a multiuser set-up operating under slow fluid-antenna multiple access (FAMA). In this scenario, a FAHM implementation with only 2 RF chains showcases a performance comparable to a fully-digital conventional multiport scheme with a much larger number of RF chains. Additionally, the proposed receiver architecture attains over 60% reduction in computational burden when integrated with a novel efficient implementation of the state-of-the-art generalized-eigenvector port-selection method.