A premium barrel will fend fouling better than most, last I knew Savage wasn't into premium barrels.
If I were you I'd contact Doug Burche at Ultra Coatings.
http://www.ultracoatingsinc.com/
He has a product called Ultra Bore Coat, I have it in one of mine and have experienced a much lessened degree of copper fouling....even with TSX's.
Ultra Bore Coat won't make a bad barrel shoot better, IOW...it ain't a magic spell. But, it will reduce the amount of fouling you get which in turn allows the rifle to shoot better longer. Ultra Bore Coat also makes cleaning simply wicked easy.
Doug now sells it in DIY kits so you won't have to ship your rifle to him...like I had to do.
Doug's easy to talk to on the phone as well, and will answer questions, offer advice and give instructions even though he's currentlyprettybusy doing work for major arms manufacturers.
Kansas time...913-829-5572