A few suggestions Hans.
All my Sav 110 LA's have a magazine length of 3.42" max cartridge loaded oal so you will run into a problems if you handload of having to seat the bullet deeper into the case. The Lott and H&H are rated at 3.60" max along with many other calibers in that cartridge size class. I'm in the process of lengthening one mag and modifying the mag mounting. Simple to do if you have the proper equipment. I have already been down the road you are now traveling and have been doing barrel switching in Savages since they first came out in 1958 or' 59 so I offer my experiences.
I'm a cheap bast** so I look for the least expensive solution to whatever problem I'm working on and reboring a barrel is a viable solution, but it is as expensive or more so than just having a new barrel fitted. ER Shaw will do the Lott, in the white, for $135 plus $30 more for polishing and blueing, up to 26" barrel length. I can hardly do it myself for that price. Most reboring is in the $300 catagory. There are many less expensive and better ways to get to where you want to go other than reboring unless you are locked into that proceedure. Besides, I wouldn't want to loose a good 375 cal barrel. If you truely want a "switch barrel" keep the 375 barrel and buy a chambered and threaded 458 cal barrel.
I would strongly suggest measuring the length of your magazine and if it is the same as all the other standard magnum mages, at 3.42" max OAL, I would go with one of the shorter cartridges like 375 Taylor or 458 WM, you don't gain much over these cartridges with the Lott or H&H, other than macho status, maybe....arguably.
One other thing. I would not use the Savage for any dangerous game. I have found that the feeding of cases with a heavy bullet out front can be problematical at the least and very dangerous if things get sticky. My 416 Taylor with 350 and 400 gr bullets will stove pipe on occasion and spit the cartridge back in my face. They are OK for non dangerous game. None of my other magnums with bullets up to 250 gr have ever stovepiped so I think it is the combination of bullet weight and the weight being way out on the end causing the occasional problem. If you are looking for a dangerous game rifle I would stick with a Mauser or clone set up as a DG rifle. You can make it into a switch barrel just as easy as the Savage.
Any receiver can be made into a switch barrel. I've done Remingtons and Rugers without any major problems. You just have to make sure the barrel is in register and is witness marked. You can even swap bolts if you match the barrel to the boltand the OAL to the magazine capacity. Any competent 'smith can do this job. I had a Rem 700 in 25-06, 30-06 and 300 WM at one time, then sold the set to do other projects. The new owner added a 375 H&H AI to the mix. I still wish he never waved that much cash in my face at a weak moment. It was a system with barrel clamp, receiver wrench, barrels, bolts, mag lifter, one stock and a scope. Took about 1/2 an hour to swap in a barrel and resight and you were good to go. The system did answer a question in my mind nicely.
Check out some of the other gun forums, there is a wealth of information available and many have already tried what you are interested in.
Enjoy