Upgrading sub to get a live feel.

Room acoustics and EQ matter a huge deal. More so than the sub hardware itself in a lot of cases.

Tim is right about the DBA/Swarm subwoofer solution. The one I built with 4 Morel 10" woofers and the Dayton amps for under $3k gives more powerful, deep, articulate and smooth bass than anything I ever heard anywhere even from vaunted state of the art speakers costing ten and twenty times as much. Using four subs spaced around the room works so much better than the old-school paradigm of one or two that it doesn’t hardly even seem to matter what quality or how much you spend, until you get to three or four you’re just never gonna get there.

I am going to join in the camp that says look at your placement and room setup before you replace your subs. That said, it is entirely likely that your subs are running out of output relative to your main speakers, which are capable of large dynamic swings. If you look at the output of the SVS-SB12 NSD (the prior model), you will see that its max output at 25 hz is 96.3 db, 31.5 101 db, and 40 is 104.6 db. You have a pair, but they are not co-located, so figure 3db more.

https://data-bass.com/#/systems/5b11db42a201f10004e39d7a?_k=8inm1d

With this in mind, it is likely if you are listening at higher levels you are running out of output. To get a set of subs that will keep up with your current speakers, much less the 4367 at full chat, you are going to have to go much larger. Whatever you get, use at least a pair, and if you have the room and money, four (distributed bass as discussed above) A few I would consider:

I think you are on the correct track Seaton Sound Submersive HP, F2, or X21.  Mark Seaton builds excellent subs, as well as monitors which are used by studios and high end home theater and music systems.  I would take the JL off the list.  Very expensive for what you get.  

Rythmik- F18 or FV18- Amazing clean, tight, and huge output. I love my Rythmiks, but I have a slight hesitation, as I think the Seatons may be a better match to your speakers.

HSU ULS-15 MK2- Boring choice, but really great quality subs that sound good and with pair, should just have enough output.

I believe that for any sub you purchase, you should be using a high quality active crossover to bass limit your mains, with a crossover between the subs and mains at about 80-100 hz. I am big believer in Richard Vandersteen’s believe that to properly integrate subwoofers, your main speakers must be linear to 1 octave below the crossover frequency, and your sub one octave above. So here, your mains meet the need, comfortably extending to 40hz.

Finally, while I don’t want to send you looking at another website, you may want to post your question and systems setup over on the AVS Forum subwoofer section. Those guys are very data driven and spend about 100x as much time as people here playing with subs. They often have very good advice on sub placement and setup recommendations. Make sure you give your room size, as it is relevant to output.

Watcher, hold on to your tater (more southern terminology) If you are going to upgrade to 4367 the subs you are using now will be totally lost.
That is one very efficient and very loud loudspeaker. Don't waste your money on stuff you won't be able to use in the future. To keep up with those speakers you will need something like two JL F212s at the least. Get your 4367s and use the subs you have now knowing you will go for the real deal when finances allow. Patience is a virtue. 

No amount of room placement ever gonna make two speakers, or even two speakers with a sub, or even two speakers with two subs, sound anywhere near as good as two speakers with four subs. Never. Gonna. Happen.

Go with four though, and surprisingly they go with everything. Placement becomes a virtual non-issue. System matching? Total non-issue.

Search around, every single one of us who has tried this is super happy. Yet the particular subs we are using and the systems we are using them with are all very different.

Why? Because it works. As opposed to everything else, which does not.