I noticed the same issue (though perhaps not to the same extent as the OP) when I started hand priming my .308 WIN and .45LC cases with the Lee hand primer.
Cleaning the primer pocket helped me a little, but I found that (as I initially used a lot of found brass and mixed brass) the most helpful thing was to make sure my primer brand and brass cases were compatible. Such warnings and instructions can be found in your Lee equipment instructions.
When they say don't mix Winchester brass and Fiocchi primers, they mean it! Took me 12 "failure to fire" rounds to give myself a kick in the pants to remind myself to read the instructions and warnings before using Lee reloading equipment.
Really? Never heard of such a thing. So what do you do if you're loading Hornady cases, they don't make primers? There's other examples where the "RIGHT
" primer is not available, or not even made. What do you do then, scrap the brass?¿
I use Winchester primers almost exclusively, they fit in everything I load. They're whats most available here locally. AND I don't clean ANY primer pockets.
The only time I had problems with priming was with 7.62 X 54R winchester cases. From their metric line of ammo. The primer pockets are too shallow. It took a lot of force with any method of primer seating tools I have just to get them flush with the case head. I plan on using a primer pocket uniformer to deepen the pockets to allow the primer to go below flush. And no, they were not crimped!