Looking for hack recommendations that have a little more stopping power than a S hack. I pretty much exclusively neck rein with a loose rein but my horse has put his head down and completely run through my S hack when he got particularly fresh. I want to know I can stop him in those situations.

You could try a Jim Warner hack, it might take out some of the bend though.

These are what I would consider a reasonably small step up from a S hack. Respectifully saying this, I think a S hack is a pretty poor design for running barrels, but I will throw one on for trail riding.

Short shanked DTE hack (or a medium shank depending on your horse) or an Ed Wright JD hack. Both of these have a lot of feel and can still get good flex  Many people also like the clampett hack. I don't like the feel of the clampett as well, but you may love it. It would be in about the same stopping power. I've never had issues stopping with them, but I'm not putting them on a run off either.

Next step up (closer to yes ma'am) - Jim Warner short shank or Pozzi short shank. Medium or long shank DTE. Also a bobby stivers, a wild child hack, or a bozo.  I personally loose some flex with these- but I've seen others ride them with phenominal feel - so its probably just me.

Yes ma'ams - Warner's long shank, ladybug, Ed Wright swivel., and the "I said F****g stop" Quick stop.

There are lots of hacks out there, these are some of the ones I have hanging in my trailer.

What is a DTE hack??

Diamond T Equine Hack, they are on Facebook. 

Thanks! I actually do mounted shooting these days so I don't have to worry about bend and such in the way barrel racers do. For schooling I still use a snaffle, but he doesn't neck rein well in those and it helps differentiate to him what we're doing.