I compliment you for paying attention.I would guess the brand name won't matter much,Lee,RCBS,etc,a lube build up would probably be about the same.
Downtown Kotzebue has what,a SuperWalMart,BigBox Discount Outdoor and Surplus,and Margarets Reloading Supply,right?
lots of case lube choices?
Just kidding.Some lubes are messier than others.Generally if you are using too much,the shoulder will show dents caused by a buildup of lube in the die.
Beware 2 things when you get your dies squeeky clean.One,they may rust if left sqeeky clean,and two,fresh cleaned,maybe not 100% dry of whatever you clean them with,you can stick a case tight in the die pretty easy.So,maybe apply a very light film of case lube to the die interior for storage.
Clean dies are a good thing.
It could be a change of case lube may help,but likely its practical to use what you have.