Sam...
With deep cuts, it's sometimes preferable to make repeated passes - with each pass removing a little more wood (perhaps 1/8"). It /can/ be done with a not-so-powerful table-mounted router, but as Puckdropper first mentioned, it's easier to exercise control with a hand-held plunge-based router with some kind of fence/guide and end stops to ensure repeatability.
Before you change/compromise your design, think about getting a little direct help from someone who already has the expertise and tools to do the job easily and who'll be willing to let you watch and learn.