I remember being able to insert a keyframe for animating vertices. This was useful especially with the Proportional Vertex Editing tools. I don’t see “Vertices” as an option anymore when I push “I” to insert a keyframe. Was that taken out perhaps because of IKAs/Armatures?
I think what you are seeking of, is still there… 
With your Mesh object selected, go in edit mode… Press “I” and then from the menu choose “Mesh”… You’ll be asked if you want to set a “Relative Vertex key” or an “Absolute” one…
Choose the one you want…
You know the rest of the drill…
I hope this helps…