Yeah use the TLE2426 as the splitting device (better in many cases than the resistor splitter) and use the BUF634 as a buffer (sounds redundant ;) ) to allow enough current to feed the four opamps.As for the rest, I have trouble figuring what you wired wrong but I would suggest that you simplify your breadboarded circuit first.
The led doesn't need to be there.
The pot has got to go.
Wire the power supply. Make sure it works good.
Wire the first part of the left channel (using just one opamp (cmoy like)). Make sure it works.
Add the second opamp in the feedback loop. Make sure it works.
Then do the same for the right channel. Make sure it works.
You had a good idea to separate the power supply from the amplifying part tho.
Try to make everything as linear as possible when wiring, it takes more space and time to do but it does simplify the troubleshooting. I like to proceed in modules (like previously exposed) and generally I get great results.
Keep in mind that a cheap headphone pair and a good DMM are your best friends when breadboarding something like an A47 amp. I learned the hard way never to trust blindly my breadboarded prototypes... I saw a nice pair of HD 540 go up in smoke... So be sure to test with something cheap (a $2 pair of headphones from Wal-Mart or The Dollar Store is all you need) and measure every voltage first making sure that nothing is badly wired...
Hope this helps!