Solder will not buff up to the mirror shine you want.
Try it on a bit of test metal first before you attempt it on a reflector to see what I mean.
For true re-chroming you should consider getting a few quotes from the local professional metal platers.
If you want the most reflective mirror finish then you should consider companies that use the vapor deposition method.
Evaporated Coatings Inc is just one that comes to mind.
If your looking for a do-it-yourself method then the spray-on chrome in a can from
The Alsa Corporation might be what your looking for.
Be sure to check out the chrome video at Alsa.