There is a difference between a CI lapping plate and a CI surface plate. The lapping plate has a cross hatched groove pattern to hold the lapping compound. The surface plate does not. The lapping plate is expected to wear and be resurfaced periodically. If your surface plate is getting worn, it's probably from using it as a lapping plate.I would not lap on a surface plate. If you do, then it's no longer a surface plate but rather a lap. Though the cast iron laps I have seen look like SP, they are not
My wife would likely even suggest it.But I can see a really major problem with using her brand new countertop for a surface plate! Unless you have a MUCH more amiable wife than I do, using her new counter top for anything other than a kitchen counter may lead to something less than marital bliss.
All the lapping plates that I have seen have had grooves about 1/16" wide and deep, cut with a slitting saw or gang of slitting saws. A much faster method, if you have a horizontal mill.The counter top is not accurate enough even if the wife would let you. I have a cast iron plate, double sided, i turned the one side into a lapping plate.I setup my mill and cut groves in it with a ball end mill, took a day of cutting, but works great.
All the lapping plates that I have seen have had grooves about 1/16" wide and deep, cut with a slitting saw or gang of slitting saws. A much faster method, if you have a horizontal mill.