You may be better off economically selling off the boards in that set.
Depending on the model, interchangeability, and rarity they can fetch a good $ on ebay.
Then again, if you still wish the project...
Use this $ to buy some simple inverters and wire them up.
Fixes the timer off problem.
You may be able to break even, or possibly gain a couple $.
You also get the satisfaction that it made someone else's tv work with the boards you sell.
All dependant on your skill and if you want to put the time into it.