I third the jumping hackamore. Tory leather makes a nice one that goes on your existing bridle, although it looks like prices have gone up. Mine was about $20 several years ago.
I have never understood the reasonning behind the cross under bitless bridles, so have never tried one…
I also ride one of my horses in the Zilco flower hackamore and quite like it.
http://www.ridingwarehouse.com/Zilco_Flower_Hackamore/descpage-ZFH.html
I usually just have a mechanical hack (https://www.smartpakequine.com/pt/english-hackamore-4412?utm_source=cpc&utm_medium=google&utm_content=shopping&utm_campaign=nb_shopping_tes&utm_term=14412) and Tory Leather Jumping hackamore (as in link above) lying around and use them on regular bridles as needed.
I have the Moss Rock Endurance Evolution bridle for trail riding and really like it. It’s great if you’re indecisive because you can configure it as a crossunder bridle, sidepull, bitted bridle, or halter. Of course, I ended up selling the extra-long reins for crossunder style and mostly use it as a sidepull…
