I've pitched this before and I don't think many have been on my side, but...
I think the easiest way they could start a transition toward babyface with Del Rio is to force him to where a mask.
I would propose that he loses a Luchas de Apuestas de Mascaras match against either Rey or Mistico(or both), but instead of him putting his hair or some other random possesion on the line, Del Rio's losing would result in him having to wear a mask.
I think this does several things... One, the biggest obstacle with turning Del Rio is his the way the audience currently sees him. His face is just so smarmy and smug that combined with his character I believe people have just grown to hate the mere sight of him. A mask helps to cushion that blow. Next, it could bring on some entertainment- he could start forcing Ricardo to where a mask as well, they could build some comedy out of that do to the fact that Ricardo has already gotten over as a comic relief presence to Alberto. Then they can make it effect his personality, Del Rio could feel humiliated, garnering him a more human appeal than the aristocrat character can ever gain. It could humble him, and eventually he could build a sympathetic rapport with the fanbase. He could then begin to embrace the mask, as well as his heritage as a completion of the transformation.
Also I would attach this to a slight change in the way he works. He could start to use his moonsault more for example and incorporate other familiar aspects of Lucha-oriented offense moreso than he does currently. It is much more natural for the young fans to support a masked luchador than it is for them to boo him. Hell, most of the kids would likely quickly forget the old Alberto and grow fond of the new version.
If the reasoning for a turn is that Vince really wants to embrace a Mexican star, the mask is such an integral part of the mexican wrestling heritage, and it will allow Vince to keep capitolizing on the kind of merchandising windfall that has always drove Rey's pushes with the company.
Apart from following the strategy I laid out, I think it will be hard to turn Del Rio with great success. I believe to much of the fanbase has just been irreversably conditioned to "hate his face".