So far, sounds like your doing really well!
Try to keep sessions short, and to the point. Say tomorrow you are going to work on a bag and a rope.
Work on the bag first - introduce it, allow him to sniff, take it away. Reintroduce it, allow him to sniff, rub his shoulder - if he moves (and by the sounds of it he will), keep with him - no yelling, and no
Reason for no talking?
It's tempting to just say 'wooaahh boyy, steady now .. come on, it's not that bad' - this is a reward. Soft, soothing voice = it's ok to this.
Or "Would you stand the heck up, horse? For heavens sake, stand up its just a bag" - angry voice = there is a reason to be scared.
Not saying you ARE doing this, but it's just something to be aware of.
If you feel you need to talk, talk to him like you would to someone who is afraid of patting a horse.
"Come on - it wont hurt! See, it's really friendly after all" Happy, positive voice. Your horse may then lick and chew and relax a little.
After rubbing the shoulder, take the bag away (behind you), pat horse, make a fuss, repeat. Aim of the session is to get him to accept the bag on BOTh shoulders (remembering for horses that what happens one side doesn't mean its ok for the other side).
Then move onto your rope work . Rub all over the body, then swing the rope (away from horse), then rub. Approach, retreat.
Just some thoughts :)
As far as bending, you just gotta keep doing it; do it more, right now on the 'bad' side, so that he loosens up the muscles on that side. Do it on the right side too, as you always want to work each side, but really focus on the left.
I would not be pushing your horse to do more bending on the stiff side, as this may a) cause problems physically b) create further problems c) hurt the horse. There may be a muscle problem going on and that is why he is stiff, and it may be in the neck/muscle/rump .. I'd get a massage therapist (if you can) to check him out first.
Suppling the neck and loosening takes time. Start off by before working, give your horse a nice rub on both sides of his neck - flat palm, rubbing and stroking DOWN his neck (or with the muscles). This bring the blood flow to the muscles increasing circulation, in prep for work. Basically your helping warm the muscles.
While lunging - how balanced is he? Does he stick his nose out to the outside of the circle?
Lead him in a 20m circle, then come in and dow a 15m circle, then out to a 20m circle again. Get him using his body.
Bending around cones is also good - you can do this leading or long lining (I personally do not like lunging with one line, and you can do so much more with long lining).
The one rein stop (aka nose to toe) is a nice way to help him stretch his body - but never stretch a cold muscle (so either rub the neck, or lunge before hand). You want to do it EQUALLY on both sides, regardless of what ever you do. Start off with twice each side. Doing it more on his bad side can tare a muscle.
If he can't reach his side (And he may dance around a little bit) that is fine, just as him to turn slightly, with feet still. Release, reward, other side.
Good luck. Sorry it is so long LOL