It's a little tough to imagine exactly what you have there, based on your description. Is there some reason that you couldn't have an electrician look the setup over and suggest what upgrades might be possible?

Sorry, but your description is too lacking in specifics to allow us to help you. Can you post pictures of what you are dealing with?

What kind of wiring goes to the pucks? Is it low voltage with a remote transformer? If so, you could simply replace the pucks with LV ones, with the appropriate transformer. Are your current ones dim-able? Do you notice radio interference with the lights on?

Agree with MTVHIKE, find out what kind of pucks you have and what wiring is coming out of the wall. Hopefully it is standard 120V A/C from the wall switch. For sure the contractor was in error if he placed a transformer in the wall some where where it could not be replaced. If 120V, all you would need to do is connect it to standard 120V undercabinet lights. They make really good ones that give uniform light, are LED, dimmable and can even adjust color temperature.