I have 2- 25/06. If I was going to update the Rifle I would change it to 25/06AI. Change the twist rate to somewhere around 1-7.5". Get increase of velocity with that. You do need a long action. 25/06 brass you can come by it very easy. The 30/06, 7mm, 280, 270, and there probable a couple of others cases that can be converted to 25/06. In thinking about it a little more. I would convert to a .257x280AI Case, and get just a bit more powder in the case. Peterson builds 280AI cases. So there is top quality brass to be had, and it only requires necking down the case. Or you can fire form the cases after resizing them. I am presently waiting for Peterson to do a factory run on the 280AI cases. I am having a 6mm/280AI being built. It's 1-7 twist rate and 30" heavy barrel. It maybe to much powder for the 6mm, but I have to see.
What started out to be a simple question, has turned into a project. It's fun, but look at all the different way you can go. There is several short action in 6mm that would work for you too.