One additional bit of info. I picked an autotransformer connection almost without thinking about it, because it's commonly used to use 240V loads on a 208V service and vice versa. I did a little reading about the true "bucking" connection (where the windings are connected out of phase) and found the following thread
http://www.antiqueradios.com/forums/...49657&start=20
Their conclusion seems to be that the autotransformer connection as I drew it is more efficient than the bucking connection as old_coot88 proposed, however either will work.
So basically, in conclusion, if you need to operate vintage electronics and have a utility who is giving you a stupidly high line voltage, connecting a cheap 12.6V filament transformer as an autotransformer and using it to reduce the voltage is an excellent option. It is cheaper than a variac, and in fact is cheap enough you could leave it permanently attached to a specific TV and leave your variac on the test bench where it belongs.
**safety note** The secondary windings of a small transformer may not be insulated as well as the primary. For this reason, I would mount the transformer on a wooden or otherwise non-conductive base, just in case the case of the transformer ever became "hot". Yeah it probably won't happen, but we're using something outside of what it was originally designed for so may as well be careful.
All the same though I would want to get to the bottom of why my line voltage was so high, a call to the utility is in order, since the approach of using a voltage adjusting transformer is really treating the symptoms rather than the problem. You live in the USA, it's supposed to be the best electrical infrastructure in the world... 137V is absolutely not acceptable, and it is possible that the utility will even appreciate it that someone has made them aware of a problem with their system.