You need to make and save a new brush set. Select the brush you want to use as a template and make the changes, then from the top right corner of the Brushes panel Make New Brush preset. You could then save a new brush set and use it instead of the Standard brush set which loads when you rest Brushes.
But is this the best approach to getting round your issue? You sound like an experienced user, so forgive me if I'm stating the obvious, but if you select the third and forth options from the preset list labeled Soft round pressure size and Hard round pressure size you should have nice tapered ends to your strokes regardless of Smoothing.
I know this has been a big issue historically. Especially with Cintiq users IIRC, and I'm trying to remember if this was fixed with updates. My gut feeling is that a fully updated CS6 should be fine.
BTW I can't let a thread about brushes go by without mentioning Lazy Nezumi. One of its many tricks is removing artifacts from the end of brush strokes. Best drawing drawing app add-on on the planet!
Thanks for the reply, Trevor!
Unfortunately the smoothing still seems to be superceeding every other brush option I have set and not saving along with the preset. Selecting any of photoshop's default circular brushes still gives me the same result as the custom brush I demo'd, which leads me to think it's some sort of specific issue with my system, which I'll have to further look into.
However 2 things! First, creating a Tool preset, rather than a Brush preset, did in fact save the Smoothing option to off, so it'll be my work-around for now; and second, Lazy Nezumi seems great and reminds me of zBrush's lazy mouse, so I'll definitely look into it!
Thanks for your quick and helpful answer!