How many of you resize after deburring? Does the pressure of the length adjustment cone put enough pressure on the neck to expand it enough to affect neck tension?

I've never had a problem with the flash hole tool causing flaring on the mouth. If the tool is sharp, as it should be, you won't need that much pressure to do the job anyway.

A flash hole deburring tool is just that, it's not a reamer.
All you want to do is get rid of the burr not ream and create a valley. And you only need to do it one time, once it's cut off it doesn't reappear. So just nick the burr off and your done with that cartridge.