This paper proposes a framework for the procurement of flexibility reserve from aggregated storage fleets. It allows for arbitrary tree structures of aggregation hierarchy, as well as easily implementable disaggregation via broadcast dispatch. By coupling discharge and recovery modes, the proposed framework enables full-cycle capacity to be procured ahead of real time, with guaranteed recovery and exact accounting for losses. The set of feasible discharging requests is exactly encoded, so that there is no reduction in the ability to meet discharging signals, and recovery capabilities are parametrised as a single virtual battery. Included in this paper is a numerical demonstration of the construction of the constituent curves of the framework and the approach is also benchmarked against relevant alternatives.