you will find that you will get the best results by

cutting the top or bottom half of the image ( 8192 x 4096 to 8192 x 1024 )
resizing it back to a 2 to 1
remapping to polar

fixing it

remapping back "from polar"
resizing back to 2 X 0.5

and if you use a bit of a overlap -- i use about 100 pixels
crop a 8192 x 4096 to 8192 x 1124

that way i can blend edge of the image back in to the original