We consider a moving-target defense of a proxied multiserver tenant of the cloud where the proxies dynamically change to defeat reconnaissance activity by a botnet planning a DDoS attack targeting the tenant. Unlike the system of  where all proxies change simultaneously at a fixed rate, we consider a more 'responsive' system where the proxies may change more rapidly and selectively based on the current session request intensity, which is expected to be abnormally large during active reconnaissance. In this paper, we study a tractable 'adversarial' coupon-collector model wherein proxies change after a random period of time from the latest request, i.e., asynchronously. In addition to determining the stationary mean number of proxies discovered by the attacker, we study the age of a proxy (coupon type) when it has been identified (requested) by the botnet. This gives us the rate at which proxies change (cost to the defender) when the nominal client request load is relatively negligible.