When I take my horses to a western pleasure trainer I expect them to be trained to show western pleasure. For the extreme collection required to show successfully, 4 months isn't really enough time to build the muscles that are required to carry the horse in frame. Also, he's 6 with sporadic training and riding history, so I'm guessing quite a bit of time had to be spent teaching him to go straight, since it says "he was all over the place with his body" and to get him responding to leg cues. So some unlearning and retraining had to take place too. He wasn't just a blank slate as an unstarted horse would be.
In showing western pleasure (on the Arabian circuit, I don't show QH's so they may be different here), I hold my left hand out above the saddle horn and the romal reins just below where they are joined by the quirt, so lots of drape in the actual rein part, and then I hold the bottom of the quirt in my right hand on my thigh. All of my 'steering' is done by seat and leg cues, not by moving my hand. It's actually bad form and will knock me from competition if I try to use the reins to direct my horse. The bit is, at the very least a spoon bit or a spade bit depending on the horse's degree of training. A horse over 5 MUST be shown in the bridle and horse under 5 MUST be shown in a bosal or snaffle (I haven't seen a horse in a snaffle in years in the ring). Especially the bitting and training to seat and leg cues can take quite a while to learn and polish.
So, if you just want a comfy trail horse then you need to follow up with a trail trainer (but make sure it's not an in the ring show "Trail Class" type trainer), you want a 'take it out and ride it on the trail' type trail trainer.
If you want a finished western pleasure horse you will need a year or more with your western pleasure trainer. In Western Pleasure you probably would never side pass, but you would get really good foundation on all your gaits, walk, jog, lope and back up. Then you'd go to a trail class trainer for him to learn how to negotiate the obstacles and to do that class in the show ring. At any point in time, with a previously broken horse, your trainer will probably find holes in his training. Depending on how severe the holes are, it may take one session or it might take 2 months to fill in the holes and then start to make progress. It's actually easier to start with an unbroken, unmessed with horse and start from square 1 and go from there.