Riding him bareback or not will not make him more responsive or get your message across better. And a bit of neck reining will do nothing either, you have to get your cues across stronger, and also, if this is a well trained horse, he may see no sense in the lunging, nor need it.
Is this your first horse? How much real experience do you have with horses, by this I mean, do you know what you are doing or trying to do?
The lunging craze can go too far, especially if horse is already well trained, or not inclined to act like the village idiot anyway. Most horses I feel, come to really dislike it, as I have seen people lunge an hour or more, when the horse was not fresh, not misbehaving, and not a nutcase. They could have gotten on and ridden quite easily, just felt like they had to lunge each time.
Have you done any chiro on this horse? Massage? Stretching exercises? Run your hands along his neck, shoulders and back to see if you feel any "hard" areas? Those areas will feel tougher, not as pliable. Think about how your neck and shoulders feel when you have strained it. That is the feeling you are looking for under your fingers. If you do feel that, and I expect you will, then massage those areas well, or rub your hands together to make them hot, and lay over area, cool packs (ice in baggies inside towel, or cold water only) laid over area will help, as will massage. Stretch him by giving him carrot to reach for, make him stand still, with you by girth area, and have him reach his head around to get carrot or treat, both sides, stand in front and have him reach way out to get it, and then place carrot low and do the same.
Also, if this is a former roping horse? Neck reining and subtle cues are not their forte. They come out hard and fast, know their jobs well and do those expecting the cowboy to know how to do his. These horses are basically trained to think as a team with their roper. A good roping horse will set the roper up, with the roper never having to tell him what to do.
To expect a horse that has worked like that to automatically know how to be ridden an entirely different way is wrong. Same thing as if I told you you had to speak Mandarin Chinese NOW, and got aggravated when you couldn't.
You need to work on teaching him what you want, being consistent with your cues. To teach a horse to neck rein is 3 parts braided, if you will, into one. The off/near hand, leg, and rein all move together.
Say you are riding, and want to go left. I would begin a very light tensing of right calf muscles as I roll leg slightly in by turning right toe out, at the same instant I would bring right rein against right side of horse's neck, followed a micro second later by my left pinkie reaching into left rein and barely tweaking it. And the left pinkie would only be used to get horse to move left if he didn't do it off of calf and rein cues to right side.
And when I say lightly for all of these cues? I mean exactly that, as lightly as you would pick up a baby chick. Soft cues, followed by slightly less soft cues, increasing in pressure if needed. By keeping your cues as light as a feather? You will soon have a horse that responds to the barest whisper of a cue, and to onlookers? It will be as if you and horse are mentally linked.
You can reinforce this mental link in everything you do with a horse. Moving horse over in stall, haltering, leading, backing up. Light cues, including voice cues, strengthened if need to, as needed to. Eventually your horses will move off of voice, pressure, or even you signaling with your hands.
I would lose the lunging, and ride, unless horse is cold backed, and then only lunge to get that off, and shouldn't take more than couple of minutes then.
You, as a horseperson, have to be able to figure out if the horse is saying no because;
A. Horse doesn't have a clue as to what you want.
B. You don't have a clue as to what you want.
C. Horse knows what to do, but your cues are wrong or confusing it.
D. You don't know the right cues.
This is so true of everything by the way.
This horse just needs to be worked slowly, to see if he does have any clues as to what to you are wanting to do, and if not, then teaching him, and that is best from his back to do.
And also, lose the kicking hard. That shows a horse that you can't figure out what to do, so are resorting to that, and it is very easily ignored if horse has a mind to.
Welcome by the way.
Horses make me a better person.