Seeking advice on cleaning gravestones

This summer I went back to Minnesota to fulfill an old promise involving cremains, and while doing so, my cousins and I paid a visit to some very old ancestors.  The Finseths emigrated to the U.S. from Norway in the 1850s, residing briefly in Wisconsin, then moving on to Goodhue County in Minnesota, where they began farming.  The churchyard at Gol Lutheran Church (est. 1864) in Kenyon, Minnesota has the graves of these first settlers (the alphanumerics after the names are guides to locating the gravestones on a nearby map):

This week, as I finally got around to storing the photos in my memorabilia, I realized that the gravestone I photographed was one I had photographed back in 2009.  Knut K. Finseth (husband of Margit Olsdatter Finseth), was born in Norway in 1809.  The Faribault Republican newspaper note his passing in 1884:

K. K. Finseth died, of Kenyon, an old gentleman of 83 years, was badly injured on the 30th by getting his foot caught in the gearing of a threshing machine. He died from the effects on Thursday, Oct. 2, night last. He was the father of state senator A. K. Finseth.

That's the history (posted for family), but what caught my eye this week was that the side-by-side images (2009 and 2022) reveal progressive changes in the flora:

There is some difference in lighting and moisture etc, but clearly the lichen is spreading.  What to do about it?  Would removal be more damaging than letting it be?  A quick Google led me to a WikiHow entitled How to Clean a Gravestone: Gentle Ways to Remove Moss, Lichen, and More.  Lots of info there, including these excerpts:

Check the gravestone for cracking, flaking, or chipping before you begin cleaning. If the grave has any of these problems, it's not safe to clean.... Clean a gravestone if there's biological growth like algae, lichen, or fungi because these trap moisture and they're acidic, which can damage the stone... Pour water over the stone to soak it thoroughly... Scrape off lichen, moss, and fungi with a plastic scraper. Press the scraper onto the surface gravestone and gently scrape from the top to the bottom. You don't have to press very hard to get the biological growth to fall away. To get lichen or moss out from carved letters or images on the stone, take a wooden popsicle stick or a bamboo skewer and scrape the material out... gently scrub near the bottom of the gravestone to loosen the grime. If you're cleaning marble or limestone, use a sponge that's even gentler than a soft bristle brush... It might seem counterintuitive to clean from bottom to top, but working this way prevents limescale from forming... Apply a non-ionic cleanser like D/2 to remove tough stains... Clean a gravestone every 4 to 6 years to prevent excess wear...

If I can find the time/energy to approach this project, I think I would have to start at the pedestal base and test the cleaning procedure away from the more crucial engraved letters, numbers, and design.  

Now, as I often do, I'm going to turn to the readership of TYWKIWDBI for advice.  There must be readers out there who have encountered this type of situation and would be able to share advice, including what mistakes to avoid. 

Addenda:  I received excellent replies within an hour.  Here are two links offered by a reader, the first from the National Cemetery Administration of the U. S. Department of Veterans Affairs [my old employer!], and the second a set of Best Practices Recommendations from the National Park Service.

A tip of the blogging hat to an anonymous reader, who offered a link to this excellent video that incorporates the recommendations from the other links: