Are you sure it's a 12LP4? My Mayflower is a 10" set.
It's an easy restore but there's a fair chance the Flyback will be bad.
I found the early RCA "Fly1" will drop right in and work with no mods except changing the Yoke Network to the RCA values.
The RCA Fly runs cool even after extended periods of operation.
These make a very good picture but weigh a ton, I had to remove the power supply chassis just to be able to lift it.
My Mayflower running.
http://www.youtube.com/watch?v=OXlF0haH-zY
The Flyback swap: