Why not think about concrete staining and then sealing the slab? Pick a color that blends with the deck stain the fell on it. In the hands of an artisan the results can be quite spectacular. These are interior floors but you get the idea. No reason they could not be outside. You might be able to DIY but it will take some painter's tape and layout ahead of time to get a tile look like shown in the two pictures.
You cannot sandblast or you will have pits and divets. Water will get in them and if you live in a freezing climate you are in for trouble. If you polish you will have to do it all and you still may not get the stain that dripped out of material.
Two final option would be to epoxy coat it or to paint it with porch and patio paint. Either option will not hold up as well as staining and sealing.
Where are you by the way. You might want to modify your profile to include basic location. It helps us out in responding to know what part of the World you live in.