Any thing else I need to know?
Other than that you will deservedly earn the wrath of Savage 99 fans? yes, a couple of things.
One of them is that when Savage put the .308 into the model 99, they lengthened the magazine box a bit.
You'd be further ahead in terms of effort and possibly money to just get a factory chambered 99 in .308Win.
Or, as mentioned, .300 Savage cases are easily formed from .308 Win brass.
And when Eugene Stoner and others came up with the 308/7.62x51 it was based on the 300 savage case. In fact they started with the 300 savage round and for some reason chose that 7.62x51 instead. Not sure why, as the 300 savage will do anything that will do
Stoner had nothing to do with the development of the 7.62x51mm NATO. The round was developed by the Army. They were looking to replicate the ballistics of the GI 150gr .30-06 load. The .300 Savage couldn't do it. The first prototypes for what became the M14 rifle were in .300 Savage, and couldn't meet the desired performance specs.
SO the designed the .308 case, which could, because it operates at a higher pressure than the .300 Savage.
Also, the Army was not going to adopt a commercial round. They have a LONG history of that.
If you want a 99 in .308, find and buy one. DO NOT rebarrel, or rechamber the gun you have in .300 Savage, and don't even THINK about touching the magazine. The rotary magazines were essentially hand fitted at the factory, do NOT mess with them!!
I mentioned your desire to convert to .308 to my Savage 99 expert, and he backed away hissing, and held up a cross....
Don't mess with the rifle, get a factory .308 if that's what you want.
The .300 is a fine hunting round, the 99s are not target guns, find a low power POST reticle scope and go collect deer or even elk at 300yds or less.