The Dutch healthcare sector wrestles with rising costs, staff shortages, and increased demand due to healthcare centralization. This, coupled with worsening traffic congestion, underscores the need for efficient solutions like drone-based medical transport. This paper addresses the need for effective fleet management strategies tailored to the unique demands of the healthcare environment. Specifically, it seeks to develop an adaptive strategy that accommodates the network's expansion and the inherently stochastic and urgent nature of pickup and delivery orders associated with medical transport. Utilizing an agent-based model formulation, the paper introduces a novel approach combining adapted temporal sequential single-item auctions for allocation and scheduling with reinforcement learning for drone repositioning to optimize fleet management. Our findings highlight the strategy's consistent efficiency across various demand scenarios, maintaining performance within predefined limits. Notably, the repositioning module significantly enhances the fleet utility and the fraction of served orders, albeit at the expense of increased cost per delivery. Conversely, the reallocation module causes minimal performance improvement. Under heightened stochasticity introduced by urgent orders, the strategy maintains stable costs per delivery while fleet utility and order fulfillment rates decline. Additionally, our investigation underscores the increasing benefits of repositioning in more stochastic scenarios. Moreover, exploring hybrid fleets reveals that while short-range high-payload drones can reduce cost per delivery, they compromise overall fleet utility and order fulfillment rates. Furthermore, we identify the under-utilization of payload capacity in scenarios with orders weighing up to 2 kilograms for a drone with a payload of 10 kilograms.