StackWise is the correct solution because the company needs more access ports while reusing the existing access-switch uplink capacity. Cisco StackWise allows multiple compatible Catalyst switches to operate as a single logical switching system, increasing access-port density without requiring each added switch to consume new uplink ports on the distribution layer. This fits the design constraint that the distribution switches have no available ports for additional uplinks, while current uplink bandwidth is not a bottleneck.
VSS is normally used to combine two chassis-class switches into one logical system at the distribution or core layer; it is not the practical answer for expanding one floor's access-port count from an existing access switch.
EtherChannel aggregates physical links for bandwidth and redundancy, but it does not create additional access ports when no distribution ports are available. VDC is a Nexus virtualization construct and does not solve Catalyst access-port expansion. The correct operational design is to add a stack member and use the existing uplink design. Reference topics: Cisco StackWise, access-layer scalability, uplink preservation, Catalyst campus switching.