expect to spend a lot of time
No matter how you look at it, you are going to be doing a quite bit of sand and fill work. Always remember that your LABOR is going to be more expensive than your materials.
EPS is certainly cheap, and a pain in the arse to work with, but if you are only going to build ONE part it is one way to go. To save all the hassle of spackling and sanding, you might consider using EPOXY resin and fiberglass CLOTH (not mat). Epoxies will not attack the EPS, saving you the time, and materials required to protect it. A hidden advantage to the epoxy/EPS combination is that when you are ready remove the foam plug, all you have to do is pour a cup of acetone into the cavity and it will dissolve the foam.
I’m guessing you are going to be using sheet material to develop your “plug”. I would cut out circular cross sections with a hole at the center, and then mount the sections on a section of pipe (shish kabob style) using a pressure sensitive tape to adhere the sections each other as you go. Most spray adhesives will attack the EPS. When you have assembled this mess mount it in a crude fixture that will allow you to rotate it (as in lathe), and using a template knock the corners off of the sections to reduce it to a smooth(er) surface. Starting with 40 grit sand paper start to develop the surface, finish up with 80 grit (no reason at all to go any smoother). Use your template to control the sanding process.
Using polyurethane sheet foam material, while more expensive, would allow you to use cheap(er), and more readily available, polyester resin; polyurethane foam is resistant to polyester. In addition, your plug sections could be adhered with spray adhesives.
You will need to determine how thick the shell is to be and allow for that in the foam plug. i.e. if the cross-sectional diameter to the shell is to be 600mm, and the material thickness is to be 3mm, reduce the diameter to 594mm (allowing 3mm on both “sides” of the diameter).
Cut the cloth on the “bias”. i.e. roll out the cloth on a table and cut it at a 45 degree angle. When cut in this manner fiberglass cloth will readily conform to compound surfaces (and I would consider an “egg” shape to be compound).
In addition to the advantage of cloth conforming to the surface is that cloth can be laid out on the form DRY (when it is far easier to handle) and subsequently do the “wet out” in place.
With this method, it would be possible to do one half of your egg with one piece of cloth, allow it to cure, and then do the other side.
But it is going to take more than one “lamination” to get any kind of usable materiel thickness, unless you are only going for a visual part; as in no structural load. Typically a single layer of 1-1/2 ounce cloth, laminated with resin, will yield a thickness of roughly .015-.020" when rolled out.
I’m not sure what spray on PU elastomers you observed being sprayed on … you should ask them what it is.
With regard to any “sprayed on” material it will not be inherently strong by itself; think egg shell; easy to crack. To get the strength you will need in an object of this size you are gong to need a “reinforcement”(fiberglass cloth). A vacuum formed thermoplastic ABS shell would be strong enough, but the mold would still require a “pattern” of the shape be made to subsequently make a mold from, you would require two halves that would have to be bonded together and sanded to shape. If you opted to vacuum form over a male mold, the “second surface” would still require considerable sanding to achieve final form in addition to the joining and finishing process.
