Sometimes working on the gun and making it what you want is part of the fun but it sounds to me it may be the wrong rifle to take hunting . For the amount of money you may spend on fixing this gun you may be able to buy a Ruger American or a Savage Axis . Both are well under $400 , less then 7lbs and very accurate . My American is sub MOA no problem and pretty light at 6-1/4 lbs .
Just a thought
EDIT: I was just looking at all the 243 savage heavy barreled guns they make . They all look like really nice rifles that I would not want to mess with . If it's not a heavy barrel I don't think you can have it flutted . If you can have a light spoter type barrel flutted . I would think you would not be able to remove enough meterial to make a difference .