One thing to keep in mind, whether it's a sprite or a plain - you can always change the colour to black, and the alpha to 128 (or something), and you have a shadow version.
So maybe, rather than having an oblong shadow - you could have a copy of the sprite, coloured black and 128 alpha, invert it on Y, scale it on Y by half, and you have a rather neat shadow effect. Have it move down by half the speed the player moves up - so it's like the shadow is projected.
You can also have the shadow behind the sprite, like as if the main light source is above and in front of the sprite, rather than above and behind.
I often change the colour of a sprite and it's alpha to make a shadow version - it's cheap and effective, what more could we ask
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I got a fever, and the only prescription, is more memes.