Actually... the pelham bit is the bit everyone jumped in years ago.
Few used simple snaffle bits.
Children, lead-line child riders rode handling 2 reins.
Hunter classes horses rode in pelhams...
Appointed classes the bridles were sewn in bits, headstall and reins...there were no buckles for adjusting, bridles were "fitted".
It is today when fad has taken over that you see fad bits...and bridle pieces.
3-ring gags, a this or that bit, weird crazy configurations of nosebands, headstalls that are to difficult to describe all with claims of comfort to the horse is made to separate $$ from your pocket.
I could open my ex-bosses bit box and show you things that would curl straight hair...all used and made for particular reasons...none of which to the unsuspecting eye look anything more than a simple single joint bit till you peer inside the mouth or drop the bit for inspection..
Even some of those innocent are not innocent bits to knowledgeable eyes.
Yes, a pelham would
work and you are not
supposed to ride off the curb rein either but have that to finesse a communication given and shared.
They make the exact mouthpiece you mention the horse enjoys riding with...
Look at polo bits...see it in many stores, catalog and online described as a polo bit.. https://www.statelinetack.com/item/k...bit/SLT900241/
Just remember the shorter the shank the less leverage applied when that rein is activated and the less purchase, the loop the headstall connects/hangs from, the closer that loop is to the actual barrel mouthpiece the less leverage is...
Combine shank length and purchase height and a innocent looking bit is far from innocent in any style of riding discipline..
The curb rein in English work to lighten the horse and offer extra communication to the horse in understanding...no different than a western trained horse actually.
Hence a true snaffle bit is headstall, rein and bit barrel mouthpiece all using the same ring
for attaching "stuff" to.