You didn't say whether the bit is 1/4" shank or 1/2" shank. That makes a big difference in what you can do.
Most router's have guides that you can outfit them with that will let you set the depth easily to make several passes. I use my guide on my router quite often. For a one time deal, you can probably do it if you go really slow and with a sharp bit. You may end up with chatter and burn marks on the material but it sounds like that edge won't be visible.
It's a 1/4" shank. The router is a craftsman I inherted from my father, the bits are fairly new and still sharp. I can easily set the depth to do multiple passes, but I can't envision how this will help since that wouldn't allow the bit to be 'guided' along the way.
Do this. It's not that hard to tack a guide to the bottom of the countertop and route it twice.
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Your comment just made me do a face-palm. It made me realize that I don't have to do the first pass from the top of the countertop and try to figure out some way of clamping a guide on... I can flip the dam thing over and and screw a guide in to the underside, then to my 1st pass with no fear of the clamps slipping and/or them getting in the way. Pass #2 I flip it back over and use the bearing on the trim bit to keep it flush.
Thanks everyone for helping me figure this out.