To re-barrel a T3 in 243 win That still shoots , is in my experience is spending too much . Your far better off trading it in if it still has like left in it . To be fair you can find some real nice second hand 308 rifles on the second hand market for very handy money . Remember a lot of folks hardly shoot many meaningful amounts of rounds in decades of storage.
For instance i bought a very clean .223 Sako about two years ago off Guntrader . I paid a good rifle builder to chop some length out of the barrel and re- screw cut and it cost me about £700 all in . I then bedded it and brought the wood to its very best ( probably brought better than when it was new ) .
Previously I had my .243 win Sako 75 ( i bought this one when the 75 was launched ) . During lock-down I had a well known rifle smith ceracoat fit pillars , it already had a mcMillan stock for it , that i purchased years previous . I don't mind the fact i will never get anything near what i paid for this one !
Just saying these things because you will not get anything your money back in future trades or sales .
Why are you looking for the same with a 308 win barrel can i ask ? Over the 243 win you already have ?