I know where you are coming from. I like the guy myself but his problems will not be cured on the training ground or on the pitch on match day. The guy was a fantastic player who is now questioning his own ability. I think the club would do well to get him talking to a sport psychologist regularly.
I was watching him warm up in the Europa league against ...hmmm... I can't remember actually, and he stayed out to practise a few shots with the reserve keeper after everyone else had disappeared down the tunnel. He pinged about 10-15 shots into the corners of the goal. Beautiful technique, striking right through the ball. Then he shanked one left, and then another and another and another. About 8 of his next 10 shot went left.
I see something similar with young players when they are forcing the shot, not confident in their own ability and trying to power the shot in rather place it. You would think a pro like Soldado would be above this type of thing but obviously not. If Soldado found his Valencia form again I would be amazed and delighted in equal measures.
I agree completely: his demons are mental, not physical and definitely not technical. I like your anecdote an awful lot, because it does describe Soldado absolutely perfectly, in my opinion: a player blessed with abundant technique and footballing intelligence, but let down by a certain mental fragility that is frustrating to witness. Frutstrating, not because it impairs him as a person or a team-mate: everyone largely agrees that he's a great guy, a committed player both in training and on the field, and a member of the squad that everyone seems to largely like. Frustrating, not because he doesn't recognize his impairment: he clearly does, and it's even a credit to the person that he is that he clearly doesn't seek to blame his team-mates or outside circumstances for his travails, which is a defensive reaction a lot of people fall into quite easily.
No, it's frustrating precisely because he's a great guy, a great trainer, a good ambassador for the club and seemingly fully cognizant of the situation he's in. It's frustrating because he looks like he knows it's happening, and yet he seems unable to overtake these swings in performance and the attendant mental highs and lows that accompany said swings. It's frustrating because the player he can be is held back by a mental situation that not even the good trainer and man that he is can overcome.
I'm still unwilling to write him off, and I want him to be given one more shot at this club, if only because I know that even if he fails to take it, he won't kick up a fuss and will be professional throughout. There's a player in there somewhere, a player that was on display as recently as 2012-2013. And I definitely think that the club should try your idea about getting him a sports psychologist, if he's amenable to such a thing: it could unlock that player again.