Here is a way to get the results you want, but you should know that this will also have distortions (math says literally anything will), but it will at least have distortions that fulfill your requirements.
Using the HwB
package,
distanceLong = haversine(long1, long2)
distanceLat = haversine(lat1, lat2)
where the locations are the lats/longs at the far edge of your raster. Now just enforce these distances as the edge lengths on either side of your raster (I'll let you figure that one out, but it probably involves dividing the distances by the number of cells and making that distance apply to each individual pixel). Have fun and stay safe out there #mappingisdangerous.