Here is the thing about the .375 Ruger when it was developed by Hornady and Ruger it was made to produce .375 H&H performance in a 20" barrel. So it will push a 270 grain bullet to 2800 fps out of a 20" barrel. So to say a .375 Ruger won't efficiently burn all the powder in a 20" barrel is a fallacy, but you have to choose the right powders if you reload the .375 Ruger.
When I built my .375 Ruger I went with a 24" barrel just because I was wanting a more traditional length barrel on my M70 Winchester, and the 4" longer barrel helps with noise. I can't imagine the noise from the Savage with it's 20" braked barrel. I had an Encore pistol with a 17" braked barrel and that thing caused a terrible flinch just from the blast I was receiving from the brake.
There are several options if you want to go with the H&H. I'd look for an old Interarms Mark X or Whitworth in .375 H&H these can usually be had for around $750 and get you a Mauser action. Winchester makes a nice SS laminate in the M70 Alaskan but will run you more than $1200 NIB. Then you can pick up a Browning, Sako, and the occasional Remington M700 as well.
The nice thing about the .375 Ruger is that you can rebarrel any standard length magnum action to use this cartridge. I took a 7mm RM M70 XTR and rebarreled it to the Ruger when the cartridge first came out just to try. I think it is a good cartridge but in the end I think I'd rather have the H&H just because I like the classic appeal of the cartridge and the history behind it. Plus there are far more options for brass out there than just the Hornady brass for the Ruger. Most times I can find new H&H brass cheaper than the Hornady brass.