Since this is the first seasonal hunt I've been around for, I'm not sure I completely understand the rules; on the egg hunt page
it says I can only hunt a species once, but does that mean there's only
one Uilus egg out there waiting for me to find it, or just that once the
 timer runs out I can't try again?

I'm really hoping I still have the option to find one... since the first one I got miraculously decided to fail, despite being fully incubated.

Okay phew, glad to know I still have a shot at getting one! :)