Is there a specific word (or possibly phrase) that represents a type of takeover where an individual is planted into an organization and gains trust and respect over a period of time until he's in a position to facilitate the takeover? Kinda like an inside job from the outside?
I think you could refer to such a person as a "mole" or "sleeper agent" without fear. In the parlance of intelligence a "mole" is used for any agent that infiltrates an enemy organization and attempts to gain their trust so as to weaken or disable that organization. Whether it's by the release of secrets, operational inefficiency, or other means, seems to make no difference. The act of weakening, disabling or destroying the organization could be referred to as "subversion".
To describe this strategy, you may refer to entryism (also referred to as entrism, occasionally as enterism) that is a political strategy in which an organisation or state encourages its members or supporters to join another, usually larger, organisation in an attempt to expand influence and expand their ideas and program. In situations where the organization being "entered" is hostile to entrism, the entrists may engage in a degree of subterfuge to hide the fact that they are an organisation in their own right. (source Wikipedia)
In specific cases, infiltration would be another possibility.
To infiltrate means to secretly enter or join (something, such as a group or an organization) in order to get information or do harm.