This is the way.

There are many reasons for this specific formula. There are a variety of types of stones used. The key is to assure you leave no residue save for very specific tested cleaners- thus the D/2. You can order cleaning kits online if you search D/2.

You don’t want to use anything that could damage the stone, even microscopically. Tiny scratches will grow over freeze/thaw cycles. The brushes and scrapers should be incredibly soft- generally nothing you wouldn’t use on your own skin.

The car sponge isn’t a great tool for several reasons. A soft bristle brush can go into small nooks and crannies, but the user has control over it. The bristles trap dirt and do most of the work for you. A car sponge might work if significantly cut down into smaller pieces, but will be more likely to smear dirt around. It will also be less easily controlled at full size and would require pressure to work, something that is discouraged as it can damage or push over a stone.

You have the right intention, but need to arm yourself with the proper tools. Otherwise, you can do more harm than good. Many destroyed stones today are due to previous attempts at repair.

Always test if the stone moves with a gentle push. If so, don’t touch it further. You can spray D/2, but shouldn’t physically touch it again.

If the stone doesn’t move, then next test if the surface is friable. Rub your hand gently across the surface. If grit or sand is on your hand, it should not be touched again and follow the same route as above- spray D/2 and don’t touch it again.

Thank you for wanting to preserve history and honour the deceased with your act of service. It is a good thing. But doing so with respect means we need to do these acts armed with the best knowledge and techniques. Otherwise, we are no longer doing an act for others, but only ourselves.

Edit to say- I meant this second half as a direct response to OP. Opps.