You state your looking for 50 / 50 HT / Music...
I can promise you that a 10" sub won't do movies much justice, and 12" sealed subs are pretty good for HT, but a 15" sub will cover all the bases quite nicely...
I personally wouldn't touch a 10" sub even a pair of them, they just roll off too high for HT.
Now if ported was in the mix - a good 12" or larger would be my first choice...
I had a JL F112 and it was incredibly powerful for music and movies, but just was a touch shy for hitting the low notes under 20hz, which has become more and more prevalent in movies these days... Replacing it with a Submersive has been a great upgrade in down low performance...
A pair of the Epik Legends come under budget and would likely be pretty nice and still offer good mid teens response, otherwise - a single Empire would still be my choice for that size room... Even with a single Submersive, I don't feel like I'm lacking in smooth response around the entire room...
Good luck in your choice..