0-256 is merely restriction means you need to use evenly spreaded 256 out of 65535
that then is a 8 bit grayscale image
and you can not fit this
highest point 2560 meters, water level at 650 meters.
in a 8 bit image
it needs to be 16 bit signed from -650 to + 2560 meters

you really will DISLIKE the look of using a 8bit color depth on a DEM

it will LOOK terraced or like the "stepped pyramid"

as to worldmachine and Photoshop

i do on use Microsoft software and have not used a Microsoft Operating system in over 10 years
( well a few games and wilbur using WINE )
i kicked MS to the curb in 2004/2005

mostly Blender for for node generated noise functions ( mountains and valleys )
wilbur and GRASS/Qgis for time based erosion
( r.landscape.evol & r.terraflow )
Gimp2.9.4 and Nip2 and Gmic( terminal software) for 16 and 32 bit HeightMaps

small map sets are a dime a dozen a 2048x1024 or 4096x2048 can be done in one or two days or a week depending on the details
but map sets in the 64565 x 32768 to 131072 x 65536 pixel range maps will take 6 months

the DEM is the easiest part and that will take time , coloring it takes a lot more time
for an example :
the reprocessing of the C1 Synthetic aperture radar data from the Magellan spacecraft at Venus
took 6 months for a 131072 x 65536 map
https://www.cartographersguild.com/s...l=1#post191775

This is really rough sketch of how does equator goes through map, it shouldn't go straight from left to right, some diagonals should be good
you really can not do that and have it in a real mapping format
neither "Mercator" nor "simple cylindrical" can do that and have it "work" for a planet ,that would not be able to be geo-referenced
Parts can be mapped that way but not the whole

but i think you have a "concept" a bit off
i think you are thinking of the earth's tilt of 23.5 that causes the seasons
that is not the equator line


so expect a bit of time for all the work and a rather big price tag from whoever you get to do this
big maps are a LOT of work and can eat up drive space

( the messenger Mercury data i am working on is almost 1 terabit of drive space )