This paper provides a first assessment of a framework that allows network operators to use advanced slicing mechanisms to establish bandwidth restrictions to the different flows of a multi-interfaced User Equipment (UE), even when it moves between different access technologies. The objective is to prevent individual flows from overwhelming resources available to a slice, due to the often unpredictable traffic usage (both upstream and downstream) of UEs. To realize this, OVSDB bandwidth configuration and UE-OpenFlow support were integrated into a previously existing architecture, which used Network Function Virtualization (NFV) and Software Defined Networking (SDN) to create a virtualised representation of the UE (vUE) in the operator's cloud, and handle slice flow-based mobility in a transparent way to the endpoints. We elaborate the framework in a scenario where telecommunication providers (i.e., mobile network operators (MNO) and internet service providers (ISP)) are able to instantiate network slices when requested by an over-the-top (OTT) provider. Our enhanced framework allows the network to implement end-to-end quality of service (QoS), allowing the slice mobility capability to preserve flow-based uplink airtime resources. The framework was implemented in a experimental testbed featuring 3GPP and non-3GPP links, with results showcasing the feasibility of the proposal.