So...I don't need anything elaborate with an external handle and all that...all I need is...
...something to rest one edge of some shelf arrangement on placed on each side of the cooler.
Long nails driven through the styrofoam will work...from the outside to the inside....think those little pegs put in holes to hold shelves up in inexpensive bookcases.
All I need to do is reinforce the hole so the weight will not crush the inside cooler surface. I have some brass tubes around here someplace and dowels that fit inside them.
Some 'shelf arrangement' just has to have a lip so the cartons don't slide downhill and I can use egg cartons on that 'shelf' to hold the eggs.
Then to tilt the eggs I just use the opposite side set of pegs to rest the uphill side on.