Assuming that your system really only supports EPSG:3857. That is, the Y answer:
You know that the world looks like a rectangle when rendered in EPSG:4326. A rectangle whose width is twice as high. You also know that the world (more precisely a part of it) looks like a square when rendered in EPSG:3857.
Therefore (leaving aside the distortion of the world to the equirectangular projection) you should make a small sacrifice if you want to see a rectangle as a square, and that in turn the geometries within it will not deform. The first option involves losing all the geometries that are at longitudes less than -90 or greater than 90. The second option is to create vast oceans at the poles. Being the second option less destructive, I will opt for it.
Beyond the choice, the only way you have is to transform the coordinates of all the vertices of your geometries. But transform them in an inverse way to how they transform when projecting in Web Mercator. So then, when transformed by the projection, keep the relation they had originally, prior to any process.
The way in which the meridians are rendered in EPSG:4326 and EPSG:3857 is the same (straight, vertical and equidistant lines), so you will only transform the latitude of each pair of coordinates.
When projecting the latitudes to the y coordinate of web mercator, the following transformation takes place:
y = R * LN( TAN( ( PI() / 4 ) + ( phi / 2 )))
R = 6378137 is the radius of the sphere, in meters; and
phi is the latitude, in radians. We are not going to worry about the radius, because it will be multiplied when projecting. But yes for the radians, because our input are decimal degrees and our output must be decimal degrees as well. Otherwise, we will apply the inverse transformation.
newlatitude = ( 2 * ATAN( EXP( latitude * PI() / 180 )) - ( PI() / 2 )) * 180 / PI()
latitude is the original latitude coordinate and
newlatitude is the transformed one, both in decimal degrees.
For example, we can have as input a square of 10 degrees wide by 10 degrees high, right? No! In the world, meridians are not equidistant straight lines and that is not a square! Ok, but we see that shape as a square when rendered in EPSG:4326? Yes. Well, if we transform its latitude before projecting it in web mercator, we can continue to see it as a square in that projection.