"are all the different forms of sulphur the same sulphur, and could they be made into the same elemental substance with some processing?"
They are the same sulphur in the sense that they are all made of sulphur atoms, the difference is the number of sulphur atoms (eg. comparing the
disulphur to the trisulphur). The form you are most likely to get though, will be the most stable form of sulfur. Its known as alpha sulfur/rhombic sulfur.
In theory, yes, you should be able to turn them all into a particular allotrope, but so in theory you can make diamonds out of pencils, as Hypervalent_iodine suggested. I know
you can make beta sulphur from alpha when its in the 8 ring allotrope, and from a standard sulphur solution with carbon disulphide you can get alpha sulphur.
"On a more practical level, can the sulphur present in something like eggs be extracted?"
Mmmm from eggs? You could try liquifying eggs and running that through a manganese greensand filter. This will oxidise the sulphur ,making it solid. Those filters are
a tad pricey, so I wonder if there is a D.I.Y alternative.