1. A system, comprising: a plurality of computing devices comprising one or more hardware processors and memory, wherein the plurality of computing devices are configured to: determine, by at least one of the computing devices and in accordance with a security policy of a network-accessible service implemented at a provider network, that at least a subset of administrative operations associated with configuration of a service instance at a particular instance host are to be performed at one or more control servers of the plurality of computing devices, wherein: at least one control server of the one or more control servers differs from the particular instance host in at least one security-related property indicated in the security policy; and the at least one security-related property of the at least one control server comprises a higher level of security than the particular instance host; establish, by at least one of the computing devices, a secure communication channel between a particular control server of the one or more control servers and the particular instance host; in response to an indication of a configuration request directed at the service instance, perform one or more administrative operations associated with the configuration request at the one or more control servers; transmit, by one of the computing devices implementing the particular control server, at least one command via the secure communication channel to a command receiver instantiated at the particular instance host, wherein the at least one command is determined based at least in part on a result of an administrative operation of the one or more administrative operations; receive, by one of the computing devices implementing the particular control server, a command result from the particular instance host via the secure communication channel; and provide, by at least one of the computing devices and based at least in part on the command result, a response to the configuration request.