Use a "bow" rake (heavy stell head) upside down to spread the material.
Get the widest you can find.
$25 - $30 at Home Depot.

I assume the "bow" rake is the same as landscape rake that has a 4-ft
straight metal head - one side has 3-inch teeth, the other side is
flat. It costs $39.95 in Home Depot. I believe we are talking about
the same tool. And thanks for confirming with another person that I
should be using the flat side to spread the amendment. Now, I am
confident that I should be getting a landscape rake.

BTW, spreading a thin layer of compost on your lawn every year is an
excellent way to organicize your yard along with mulching your grass
clippings and using an organic fertilizer twice a year.

Glad to hear that you also like the idea of spreading amendment on the
lawn frequently. My front yard only has 1" thin layer of top soil
(sandy soil underneath the top soil); this needs a lot of amendment. I
am planning to do this for my front yard at least twice a year (spring
and fall) to build up the top soil.

Jay Chan