Just a follow up.
I found that scaling did not produce an good egg shape, although I acknowledge that eggs vary a lot in shape. Current steps:
I made a path of a picture of an egg standing vertical, big end down.
Working on a map at 1050x1050.
Using templates already shrunk 2:1 for map to sphere.
Assemble an image at 1050x1364
Scale the top half of map to 70%; 750px tp 525 px.
Scale the bottom half to 85%; 614px to 525px.
At the center line of the top half, the bottom pixels looses opacity:
To FIX: duplicate layer, and merge.
Copy 1050x4px centered on the middle horizontal guide. Paste to layer.
Move layer underneath main image. Merge layers.
Failure to do this will leave a 1px tall crappy line at the equator of the map to sphere.
Map image to sphere, yields a ball at 531px diameter.
Select rectangle of the top half above equator.
Perspective shift. lengthen top to 373 tall, and squeeze in at top until it fits within egg path. Anchor layer.
Select rectangle of the bottom half below equator.
Perspective shift. lengthen bottom to 325px tall, and squeeze out at bottom until it fits within egg path. Anchor layer.
Duplicate layer and merge to eliminate opacity loss of middle line of pixels.
Using egg path, select, feather 2, copy to another layer.
To compensate for the slight blurring from perspective shift:
Copy image with white background to another image.
Decompose colors using HSV. Unsharp mask using 4px and .40.
Compose using HSV. Copy image to layer above original before crop.
Set HSV layer opacity to 30%.
Select egg path, feather 2, copy visible to new layer.