@Oofta
I'm curious if you're aware of the passage in the DMG p. 251 under Areas of Effect: "If an area of effect is circular and covers at least half a square, it affects that square." Following this guidance produces snap-to-grid templates slightly more generous than the images you posted.
Yeah, any template like this is going to be a compromise, it's not simple to put a circle in squares and have it make sense. A better option is hexes, but that's not very common.