The direction you feed the router into the material in this situation isn't gong to matter, because one side of the flutes will be climb cutting no matter what direction you work the router.
I suspect the bit you're using isn't as sharp as it could be or you have the router speed set too low. At low RPMs the router will tend to follow the direction of the grain, just as a dull bit will. A sharp router bit will cut with very little effort in any direction you push it.
When I make roll top desks I use a piece of plywood as the template that has a 1" slot cut in it, I simply clamp it to the work piece and using a router with a corresponding bushing so that the slot traps the router from wandering. Also, I use a downspiral bit, so that it leaves a nice clean edged groove, and I make 2 passes to get the required depth.
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Happy Woodworking!
Tony
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