What a difference, looks great!

Try looking at Marathon Hardware or Richelieu Hardware online as they have a selection of replacement external mount hinges that might work for you.

Did you look at Ikea for lighting? They have some really low profile strip lighting - I can't quite see from your photo whether you have a valance under the cabinets or not.

Lee Valley Tools has both hinges and lighting strips, but are Canada based which may not help.....

I don't think you can change side hinges to rear hinges -- the doors need to be wider and drilled out for the hinge mechanism, and the box needs to have no lip on the side (so that the hinge can connect to the side wall). Maybe there's a specialty product for this adaptation, but I've never seen a regular mechanism.