re: Rooms with high ceilings and no overhead light - who has the best solution?

Attic above it or is there a floor above it?

If there is an attic it should be farily easy to catch a circuit and add some LED can lights. If its a lot of trouble to fish the wall use a remote switch.

If there is no attic opening up the walls and ceiling enough to hide wires is the preferred method.

Neither is cheap.

If it is tray ceilings do you mean there is a soffit around the perimeter with a lower ceiling and then a step up to a higher ceiling? If that is the case doing some LED strips along the step should be pretty easy. Its also really easy to hide wire along most tray ceilings....keep it close to the moulding and run it neat and its possible to make it look like part of the moulding...or, if not, add a strip of moulding and hide it behind it and fish the wire from the tray to the higher ceiling and do can lights. or put them in the lower ceiling. Or do both. Its not going to be cheap for an electrician to do it but it is easy enough for them to do it....since your aasking I am assuming it is not something you wanted to do yourself but if it is it is not overly difficult....cut small holes, get a fiberglass fishing rod from HD (not an actual fishing rod) and get after it. Its a pretty simple if tedious process.