To me it sounds like you have a reloaded 30-06 round. Being fired and reloaded can change dimensions, and allowing for slight measurement errors ( we are talking about hundredths and thousandths of an inch) your measurements are almost dead on. All measurements are just shy of factory, except neck dia. Also the wildcat is reloaded using 30-06 cartridges.
bullet dia is same as 30-06
case length is off by .011"
case dia at base is off by .0057"
rim dia is off by .004"
neck dia is over by .0343"
shoulder dia is off by .008"
rim thickness is off by .003"
overall lenth depends on the bullet and who loaded it
If it has no markings on it I would doubt that it is an American made cartridge. It could, however, be a foreign-made example of an American cartridge. I would bet that it a military round of some sort. I will check my Cartridges of the World book when I get home.