This is more like a job for a drill press or mortising machine with chisel bits. If you're only looking for an inch depth that and good, sharp chisels will get the job done.
Yes you can use a SHORTER router bit for this in a plunge base. Just make sure you have a well lined up straight edge for the router. Make a mark at one point on the rim of the router plate and keep that against the straight edge, or use a square router plate. Alignment is easier on a drill press with a fence
Really long bits like that are something I rarely use, only to cut a dado in many passes. You have to slow down a bit like that as well.
If you don't have a drill press now, check out the larger model WEN bench top press, which is identical to the twice as expensive JET. WEN model 4214, 12 inch bench drill press. This runs about $300, but I got mine from Home Depot, delivered to the store just a little cheaper. This has a long enough plunge to do the trick. You will want to mount a table on it and a clamp on fence (2 inch angle iron or extruded aluminum L shaped, will do, or a really square chunk of wood).
You could also get a kit that lets you drill and chisel in one operation on the drill press, although some folks aren't impressed. But it is likely the drill press is your best answer, including use of a very sharp, high quality chisel. Watch a video on the topic to see how it's done. Note that you don't use a mallet with the chisel, you slice the excess off instead using just hand pressure. Very good control that way.
The more I do, the less I accomplish.
Last edited by DesertRatTom; 07-24-2017 at 11:25 AM.