Now, before you start to get worried....something similar happened on my V-6, NOT the LS-1. I thought the water pump was going out, because of a wierd rattle when I started the car up. When the car got warmed up, it would go away. In fact, it went away for like a month....and came back. Since I have a connection at the dealer to get super low prices, I checked my friend to run a mechanic diagnostic before I ordered me a new one, to make sure I was on the right track. They had the car for 3 days, before they could figure out that it was not the water pump. They also told me that it was something internal with the engine and they would have to crack it open to know exactly. Even at my discount, I was warned $3k~$4k. I paid my $30 nostics fee and split. So, I sold the car as is and got $5,500 and this was just a couple weeks ago. the car at 84k miles.
Now a T/A is a whole other animal. If they told me that, I would order all the lower internals and tell them to rebuild it with all high performance stuff. That is if its the problem. Since the water pump replacement didn't work, I would consult either a LS-1 PRO or the dealer, no one else!!!