sorry to hear someone hit your truck w/ eggs. Unfortunately egg shells do a lot of damage to vehicle clear/paint. They create a lot of micro scratching that cuts right through the clear. The shell does more damage than the actually yolks, but you still need to make sure you clean the area that has egg yolk on it b/c the enzymes can certainly do a lot of damage if left on the paint.
Unfortunately, correcting the damage caused by the shells may not be possible. You may be able to improve upon the defects, but a full correction is pretty rare if you were hit hard. I see that you mentioned having a pc to work with, thats a good start. Did you mean you have 6" pads? or 6oz's of a product? I'm confused. Anyway, If you'd like to give it a shot at correcting the shell marks, you'd essentially want to start w/ an aggressive compound on a cutting pad. IF you have 4" pads to work with, thats even better. I'd say optimum hyper compound to start. Follow that up w/ a less aggressive polish such as ssr1. That should clear up any hazing the ohc causes. (ohc finishes really nice for a compound). Just use the ssr1 on a polishing pad. Then move to something like red moose glaze. Glazes can help hide defects. Then just top with a carnuba wax. I can't guarantee that you'll have improvements though. Like I said, egg shell damage is tough to correct.
You still may want to give the affected area of the truck (from the yolk) a full detail though, just to try removing as much as possible. Go ahead and do the standard, wash, clay, wash, polish, (then finish w/ last step process of your choice).
Hope this helps. ... lemme know if I can help set you up w/ anything.