I build custom rifles for a living and converting a military Mod. 98 to a .375 can be done and if done properly it will be safe and feed, extract and do all the other stuff perfectly. However, this work takes time and one has to know what they are doing. Time equals money and as has been said you can buy an action which is already set up for the longer cartridges for less then the price of converting a standard Mauser properly.
True the Mauser will end up being a unique rifle with an action style of it's own, the same can be done with the big P-14 or P-17 Enfields but all are very labor intensive. If you want to see what can be done with these actions check out the gun build at customguns.us. If you do want to go with a military action for the big stuff look long and hard at the P-14/P-17 actions.