The trouble you're describing sounds like the lube is the problem. If a case will start into the die you should be able to size it unless there is something preventing it fdrom going all the way into the die, like having the expander/decapping rod adjusted too far down.
I am not familiar with redding lube, whatever it is you should get rid of it and get some new stuff. Nothing is more frustrating to me than having to remove a stuck case from a sizing die.
I like the spray-on type case lube. The old pad-and-goo types are messy and it's easy to get too much on the case; they are slow too.
The Frankford arsenal spray-on lube is what I currently use, one bottle will easily do 1000-+ 30-06 size cases. It is basicly lanolin mixed with solvent, probably alcohol, to make it sprayable. Be sure to shake the container before each use. I get this stuff from Midway.
You simply put a single layer of cases in a box-I like to use one 12"X12" with 3-4" high sides; I tape the top flaps of the box to the inside and the bottom flaps down, to keep cases from "hiding"under them, then I line the box with a paper towel; put a handful of cases into the box and squirt a shot of lube onto the cases, which should be lying on their sides, but don't necessarily HAVE to be since this type of lube "migrates" over the case. Shake the box a bit, then give them another shot or 2. Pour the cases into another container, and repeat until all your cases are done. You want to wait 10 minutes for the solvent part of the lube to evaporate before you begin sizing cases. If it ain't dry you will stick a case. You want to use this type of lube in a well-ventilated area like the garage or shop, unless you really like the smell of alcohol.
This stuff also works great on the necks, the insides of which should be lubed too. Simply shake the box with the cases in it so that most of them are standing mouth-up, and spray a bit into them. You don't need to get them all since the lube will coat the expander ball after the first lubed case is expanded; don't overdo this as a little bit goes a long way.
After sizing, trim to length if needed and scrape the primer pockets clean of the primer residue, which is very abrasive.
Tumble the cases in clean(or pretty clean) corncob to remove the residual lube and grit, shavings, etc., and they are ready to refill.
For small batches I use Imperial sizing die wax which is applied to the cases individually by simply getting a very small amount on the thumb and forefinger of the hand youpick up cases with to put them into the shell holder. This stuff is also available from Midway; I don't know how much it costs nowadays since the 2 tins of it I bought 6 years ago are still almost full--I'm about 1/2 way through the first one