Sounds more to me a training issue...his and the rider he had.
People use strong bits to cover-up holes in training by muscling the horse through/past it not by taking the time to fill in the lacking education and training that is weak.
The horse after a fence landing then throwing the head also makes me instantly think he can be forward & free moving with a big stride and scope over a fence...when he landed he got popped in the mouth, in turn he learned to throw his head and ask/grab the reins to save his mouth from pain.
Rider error, horse self-preservation...
Expect to find holes when you take him home and really work with him in his training, and his training need to tweak to your strength and weaknesses as we all have those issues ourselves...no one is "perfect" in riding, no one.
As for the bit...3-ring elevator to a simple d-ring is a huge back-off.
Be prepared you might need to find "more" bit so you can ride and work together as you fill in those holes I mentioned...
Till you do some serious schooling now he is yours to truly find out what it is you sit upo,n discovering what bit the horse responds to lightest in contact needed doing your bidding with eagerness...trial and error a bit.
Borrow bits if you need to find a different one as they get expensive fast...
Don't discount riding in a Pelham bridle which can be many mouth configurations with as simple as direct reined snaffle or used with the curb rein engaged which gives you some leverage for lightening and more refined communication and honestly, some oomph since he rides in a 3-ring elevator that is oomph of poll and jaw leverage depending upon how those rings were engaged in combination.
If you use a Pelham, ride with 2 reins not
the converter strap...if you don't know how, learn how to hold and use those reins independently and in combo..delicate the communication can be, a twitch of a finger..
You mentioned a "hunter bridle" and Pelhams are a hunter bit and legal in the show ring, looks a lot more refined than a clunky converter strap too.
Thefigure-8 noseband...horse may have a habit of crossing his jaw, opening his mouth ...all lead me back to his "self-preservation" and protecting himself from someone with harsh hands and balancing on/in his mouth
Congratulations on your new horse and enjoy the time learning to be a team working together.