.30-06 really shouldn't be a problem. Even somewhat dry ones don't usually stick unless they came out of an autoloader or such. Razorhead and KareImp are right on in their advice. My first guess would that you either didn't apply as much lube as you though or their is a problem with the shellholder.

The RCBS stuck case remove is pretty inexpensive and easy to use. i think we all end up buying on sooner or later. I didn't need one for 25 years until last year.

I've used most flavors of lubes over the years including most of the sprays. The sprays are pretty good but for most chores I use Imperial Sizing Die wax - it's easier and works great. For known tough problems (i.e. '06 cases from an autoloader) I still go back to the pad and RCBS goop.

As for inside case necks I use a dedicated brush as KareImp mentioned and either Imperial or RCBS goo. I found the mica to be nearly worthless as a neck lube.