I'm going to take a wild guess at what's happening, based on what I know of thermodynamics, (but I could be wrong about the whole thing)
When a cakes and bread bakes, it bakes from the outside ... as it forms a crust, it can no longer rise. (for yeast breads, this is why we slash the top, so it can get a little extra rise out of it)
With a cake, as the sides set, it'll continue to rise in the middle, creating a domed top. With a metal tube pan, the heat from the outside of the pan conducts to the middle of the pan, so the middle will set shortly after the outside.
...
With the silicone pan, you've actually got an insulator ... the heat's not going to conduct to the inside, so it's going to be able to rise longer than around the inside -- basically, the domed cake, but you've got something for it to stick to, so it doesn't fall back down as it sets.
As I don't think the issue is distribution of the batter, I'd recommend trying other techniques to reduce the domedness of the cake -- cook it at a lower temperature (try 25F / 15C lower) for a longer time. You can't remove the problem entirely, but you might be able to reduce it.
I'd also look at the instructions that might've come with the pan -- it's possible that they have reommendations on how to deal with the problem. (and it's possible that this might not be as significant a problem in convection ovens, but replacing your whole oven for a set of pans is kinda silly)
Structure is the main reason a tube pan is used for angel food cake. Angel food cake rises a lot, but does not have much of any gluten network or other means of supporting this structure. The egg whites can hold the air bubbles initially, but will lose them eventually. (Hence you should not delay baking after the batter is mixed, and you should treat the batter gently, spooning into the pan and taking care to not slam the pan around.) The tube pan helps because as the batter rises, it can "climb" the pan, sticking to the edges. This is also why angel food cake is left to cool upside-down in the pan for an unusually long time; it should not be removed from the pan until it is completely set. If it weren't for the tube, the center of the cake would not have anything strong to hold it up, so it would collapse. This is not an issue for cupcakes because they are so small.
Best Answer
Will it will fit is an easy one. Go here: http://www.joyofbaking.com/PanSizes.html.
All but the biggest tube pan is less volume than a 9X13X2 pan.
As for how long it will bake- I don't have the ability to compute the exact new bake time; however, the rectangular pan will produce a thinner cake so the baking time will be reduced.
I would put it in for 3/4 the recipe time and then start checking it at 10 minutes intervals.