Wes
What you were suggesting in your picture is really an "outie" manifold. Whether the manifold is exposed or hidden you still need enough rear volume for the total number of drivers you use. The rear volume is your IB enclosure.
If you have easy access behind that wall I'd think about hiding your 4x 15" drivers in a conventional in-wall opposed-driver manifold. This is much more likely to satisfy your partner than an exposed box.
Then you cover the manifold opening with a colour-matched metal or wooden grill or a framed cloth grill. The grill will become instantly invisible if it's the same colour as the wall. So the actual grill size becomes a non-issue.
The IB will go into stealth mode and not take up any room in your HT. You will surprise everybody (including yourself) with your outstanding bass. Nobody will have a clue where all that bass is coming from. The drivers will also be safely hidden from curious sticky fingers.
If you'd really prefer to show off your drivers (and why not?) then by all means make a 2 x 2 opposed-driver "outie". If you want to see your drivers even better from your favourite seat then think about a two-sided manifold that sets the drivers at 45 degrees to the back wall. You won't get quite the cancellation of an opposed driver manifold but it will be better than an array without taking up all the all space of a vertical array. Arrays don't have to be either vertical or horizontal. They can also be blocks of drivers if it suits the situation better. Here's a couple of quick ideas.
Pointing the drivers into the room or at the listening position or even away from you really won't make any noticeable difference. Nor will facing them opposite ways on an "outie" manifold. Provided you have all your drivers in phase they don't care which way they face. They'll still do their bass thing.
Bass is non-directional if crossed over below 80Hz. Your speakers look easily capable of an 80Hz crossover to your IB with loads of free extra headroom.
4 x 15" PE drivers should blow you away. The PEs are close to my AE IB15s and my 4 can easily manage incredible bass.
If 4 x 15" don't satisfy then just add more drivers in pairs as funds allow. They don't all have to be driven by the same amp or the same channel on a two channel amp. Just keep them all in phase and ensure you have enough volume behind the manifold wall to take all that backwave.
All the longthrow drivers give you is more swept volume per driver. So the manifold can be more compact because you need fewer drivers for the same effect. You can easily make up for this with the PE drivers just by adding more until you are satisfied. It just takes up a bit more room, that's all. Which hardly matters if the manifold is hidden out of sight. If you do have your drivers visible then you get to show off more big drivers than the guy running just two longthrow 15 inchers.