If you are rightly concerned about chucking expensive absinthe down the drain then consider straining into a shot glass and serve on the side. The roughly...
Instead of doing a rinse with the absinthe, use an atomiser and give 2-6 squirts depending how noticeable you want it to be. I’ve started doing that and the advantages are you get a much more even coating, as well as using a lot less per cocktail and discarding the leftover. An absolute game changer.