In that case, it probably seems like the NR1607 will work for you as long as the sensitivity is above 90dB.
And with that, it looks like the Klipsch is the best bet. If you can, go and listen to them before buying preferably when you can sit down and listen for a good 15-20 minutes and a healthy volume. You'll be looking at the "Reference Premier" (RP) line, specifically it's the RP-160m bookshelves and RP-250C center for your main LCR and the RP150m for the rear if you can though any speaker from that line will give you a good indication.
Looking a bit closer at your sketch of the room, it seems like the shelves for the side speakers are up above in the vaulted area (assuming that is what you were trying to convey)? If that's the case, they won't be very effective as side surrounds and you should limit yourself to 5 channels unless you want to run some wire along the wall (or redo the in-wall wiring) and reposition the side surrounds.
So looking at 5 channels right now:
Marantz NR1607: $700
Klipsch RP-160m: $550
Klipsch RP-250c: $370
Klipsch RP-150m: $420
Total: $2040
The NR1607 is a new model, if you don't mind you can get the previous model the NR1606 for $500. If I remember correctly, there weren't any major changes between the two and depending on when you purchase, looking around you may get it for cheaper. Just remember to make sure it's an authorized dealer. For that matter the speakers also go on sale occasionally if you're willing to wait a little bit and see.
Now, for the sub(s). As said before, you have a rather large space which means you need a capable sub(s). This isn't so much to shake the whole house though certainly that can be a goal, but more so the reason being that you want the lower to mid-bass to be balanced with the rest of your speakers. You'll be using a crossover right around 80Hz between your speakers and sub which means that the sub will be handling quite a bit of content other than that low end rumble that starts about 30Hz and goes down to whatever the lowest the sub can play.
For context, the lowest note of a piano has a frequency of 27.5Hz. The double bass, tuba, bass guitar and harp play down into the 30's, quite a few instruments play under 70Hz. Most pipe organs have a 16Hz pipe (and as a fyi, there is at least one organ that has a 8Hz pipe). So there's more to a sub than just getting some rumble and boom.
So...every bit of that $3000 budget
:
Reaction Audio: Echo 15 $999
Rythmik Audio: FVX15 $999
Hsu Research: VTF-3 MK5 HP $799
The comparisons are Echo will have the most output of the three with the Hsu will most likely have a bit more output than the Rythmik, the Rythmik is servo controlled which helps reduce distortion. There's good reasons to go with any of them.
Since you mentioned a baby I'll give another choice. Though there's no way a toddler can tip over or do any real damage to the cabinet for the above subs other than scratches, but they are front firing so there's a chance that accidental damage could happen to the cone/surround. They certainly can take some abuse, but a toddler full sprint and falling into it with a toy could puncture it or do something else. Personally, I wouldn't worry about it, but to give an alternative, you could get 2
VTF-2 MK4s from Hsu. They are $560 each, though most likely you'd get a little discount for a purchase of two. These have downward-firing drivers so virtually no chance of accidental toddler damage. This sub certainly is not in the same class as the others I listed, even having two of them do not match up though it's starting to get close.
However, there would be a benefit going that route. As the frequency gets lower, surfaces have more of an impact with what's going on. So what happens is, even if you play a steady note, as you walk around the room you'll find that it gets louder in some spots and softer in others. Having two or more subs helps even that out.