Re: Can a 10 wt rod handle all of this?
A 10 is an excellent choice for the fish you wan to chase--- add striped bass to that list too if you're anywhere near where they swim. And you could also add stuff like cuda, jacks, snook, bull reds as well as sharks to 200lbs or so if you run into them on the flats.
The reels that are paired with 10 weight outfits are also a step up than reels generlaly matched up with 8 and 9 weights, in that they'd typically hold 200 yds plus of 30lb dacron backing as opposed to 200 yds of 20lb for reels matched with 8 and 9 weight reels (by comparison reels matched to 12 weights typically hold 300 yds of 30 lb reels). You can of course increase backing capacity by going with thinner diameter stuff like gel spun.
A 10 will generally be a lot easier to cast than a 12--- and if you're new to chasing tarpon, you might find a 10 is a better choice since the first priority is getting the fly to the fish. You can still put a lot of steam to a fish with a 10 if done properly, especially on flats where you don't have to worry about pumping a fish up from the depths. Where it becomes tougher is chasing small tunoids like yellow tail and any of the bigger ones like 60lb or bigger yellow fin or blue fin tuna that might dive very deep off shore.
If you do decide to chase big tarpon or off shore stuff in "civilized" places like the Keys with a decent tarpon guide, you can also use the guide's heavier 12 weight outfits. (I know the Keys barely qualifies as civilized.... ). The same is true of you're going to chase big game off shore -- again if you're going with a guide that specializes in fly fishing--- this may be more of an issue in remote destinations like baja, belize, panama etc and it's always best to make sure suitable tackle will be available in advance.
I agree with Mosca, an 8 and 10 will cover a lot of situations in SW, so a 10 would be an excellent addition to the 8 you already have. Although you may want a 12 down the road at some point, it's utility is much more limited, and so it would be a much more specialized stick--- and again for most of the stuff you'd chase with it in many destinations you could probably use the guide's gear if you needed it. Good luck!