I'm with Dave on using that method.
Score quality lines with the knife, then rest a wide chisel in the lines depression, hold upright, and give a light tap.
Best if the chisel is the full width of the line, as with the ends of the cross.
Then cone in at a shallow angle and flake off a small amount that will intersect with the bottom of the cuts from the chisel taps.
The bevel on the chisel will eventually force it away from the center of your inlay area the deeper you go, that is why you take light bites when starting.
Process is repeated until you are down a bit (maybe 1/16").
After that you have a clean border established and can get more aggressive.
The router plane is susceptible to grain tearout, but for the edges, the bottom of the chisel cut should be equal to or greater that the router planes depth (i.e all surfacing cuts should intersect a pre-cut line of severed grains).
For the bottom of the "pit", a router plane will get you close, but as you've discovered, tearout is an issue.
The router bit in the inlay kit will alleviate this problem since it cuts with a rotating bit versus the router plane.
Of course if you plan to fill the area with alternate woods/material, any tearout will be hidden and just your clean edges will matter.