If I have a 7 mag and there is .188" of freebore cut into the chamber, I essentially have a little bit more case capacity. With more powder in the case, is it safe to say that I would want to use a slightly faster burning powder because of the increased powder capacity to ensure it all gets burned up?
What I'd like to try and do is explain the error in your logic. A faster powder hits its peak pressure quicker. More of a faster powder will hit a higher peak. That is often a bad thing.
A slower powder hits its peak slower. Large overbore cases contain more powder (due to the increased case to bore capacity) and generally do better with slower powders. This is especially true, when shooting a heavy for bore projectile. So lets say you opt for some 195 grain EOL in you 7 RM. Likely, you'll opt for a relatively slow powder, since its going to take some time to get that heavy old bullet with lots of bearing surface moving. Don't want to peak fast.
If you have decided to shoot some 100 grain bullets in your 7 RM, (I don't know if they even exist, but for comparison sake, I hope so), then those short lite bullets have far far less inertia, less bearing surface, and probably, a lot more free bore, so the bullet gets up some momentum before it hits the rifling and engraves itself (which spikes the pressure). Less pressure spike if the bullet is already traveling at a decent speed when it hits the rifling. Thus, you *may* get better performance with a faster powder when shooting light for bore bullets.
All things being equal, having a longer freebore, DOES potentially allow you more room "at the top" when working up loads. For two reasons. You have essentially increased the cartridge case capacity, since you are not seating the bullet as deep into the case. And, by having a longer free bore, your jump to the rifling can be maintained. But BOTH these factors should be experimented with very cautiously. Going over book loads gets done all the time around here. By very experienced shooters and by fools. Not always mutually exclusive. Be careful.....
Oh, and one more point. Reloading manuals work up and show charges in a variety of powders, so that hypothetically you don't need a gazillion different powders to shoot all your different guns and bullets. And reloading is trial and error. I am am sure that someone out there is shooting RL15 in a 7 Mag with a 180 grain bullet and its accurate as heck. But just cause your manual gives you 7 choices doesn't mean that there isn't a best choice to start with, which can be found using some research and understanding first.