If you have a 7mm Mag I think you already have the longest throw, and longest mag, that you can have.....
Shorter actions are considered more accurate due to less flex, etc, but in the case of the tikka that doesn't apply. That bolt stop doesn't make a SA T3 functionally any different than a LA.
The modification comes into play if you have a .308 length action, or .300WSM (like me), and you want to load rounds that wouldn't normally fit into the mag, or get snatched up by the bolt when you pull it all the way back.
This is what I've learned....
You can modify the bolt stop by either getting an overpriced and hard to find new one, or taking it out, and making a simple mod. YouTube vids are easy to find on this.
The mags are a bit tricky. From what I can tell they're all the same length overall, but have different length spacers in the back end of them. They're not all the same inner width, however..... Apparently if you try and make a 30-06 mag work for a .300WSM the .300's will be too snug and not pop up properly. There are mods described for the mags on YouTube, etc as well. I had a spare .300WSM mag so I had a go at modding mine the other night....so we'll see how it works here soon.