After sanding, sanding and more sanding with 60 grit sandpaper on my half sheet sander, i eventually got rid of the saw marks. I then cut the slabs into nice sized cheese/bread/salumi platters and continued sanding by hand with 100 grit sandpaper. Making sure to round over the sharp edges and corners:
I then moved onto 150 grit sandpaper, then 220 grit sandpaper. The platters were starting to feel really smooth, and with each progressively finer sanding the grain and figuring in the wood, began to emerge:
I applied one coat of chopping board oil, using a clean cotton cloth. Then rubbed off any excess.
After allowing the oil to penetrate and dry for several hours, i sanded one last time using 400 grit sandpaper. Then cleaned off the dust, and applied a final coat of oil. Now you can really see the beauty of the walnut's grain:
So there you have it. I ended up making 10 platters using $20 worth of lumber, $20 for a can of oil and about 60 hours worth of sanding. Hope they get years and years of use.