There's no way a 120 Volt AC would read 388 Volts The maximum peak Voltage is 170 Vp so that would be 340 Volts DC in a voltage doubler like the Sony power supply is supposed to be.
Just how dirt cheap did you go with your new lamp? $200 cheap or $75 cheap?
I prefer all Lamps be from the original manufacturer, because they are about the only ones' that actually work 3 years without causing the customer to think their ballast is bad, or something else....
Most TV lamps are $200 for Sony originals
Here's your lamp --
Now, does your lamp ARC then immediately go out without MAINTAINING an arc?
That's a Lamp with no gas in it at all.
Some will maintain an arc for 20, maybe 30 seconds then go out.
Others will get past the 2 minute stage, and go out two, three times a day.
The point is that lamp must maintain an arc and a good lamp will STRIKE , then RUN, and stay running until you turn it off.
And to be honest -- I have RARELY had to replace a ballast let alone a voltage doubler in a SONY.
In fact, I've NEVER had to do that to your model, let alone all the Sony models out there.
Samsung Yes -- Sony NO.