I prefer sealed subs as well. They aren't as popular because they don't go as low and don't play as loud for the same driver. It is hard to imagine why people are worried about bass extension for movie LFE. All of it seems to be above 30 hz, most of it way above. I solved the issue by building a 15" sealed sub. It goes into the mid 20's in my room and moves enough air to shake the room enough to cause you to catch your breath. My room is the same size as yours. More than enough for me. I'm not interested in breaking windows. It sounds better than any ported sub I've heard but, of course, I haven't heard them all.
Personally I don't see a huge problem with having a sealed and ported in the same room as long as they are phased and level matched for movie LFE. For music it might not be ideal because the ported sub would react differently to changes in level than the sealed sub. i.e. volume levels might be inconsistent. You could simply turn one off for music listening.
You have a healthy budget. You might even be able to find a pair of sealed 15's within the budget. If you spend it on a pair of ported 15's you are also likely to get pretty good sound because the better ported models do sound better than the budget models.