The first problem I see is the 12.44 you're looking at is a dual 4 ohm coil design. How do you plan to wire it? Your current plate amp won't like a 2 ohm load which leaves you driving an 8 ohm load with 280 watts.
Secondly, what improvement are you expecting compared to the GR-Research SW12a. I modeled the 12.44 vs. a SW12a in 2.4 tuned to 19hz...I'm too lazy to run as PRs, especially since GR doesn't publish the necessary specs to complete the WinISD model. Should be valid for the purposes of this comparison. The SW12A actually has a slight (2db or less) output advantage above 22hz. The SW12 doesn't hit Xmax until about 16hz, assuming no rumble filter, which I think the Apex Sr. should have. So, it's only below 16hz that the 12.44 would protect you from Gain Knob Abuse, again, assuming no rumble filter.
Given the models, are you sure you bottomed the driver?
PR's have limits too and should make some sort of noise when they get there. In my experience, a clipping amp can produce a sound that's resembles a bottoming driver. Unless you've modified the Senior, it comes with 6db of boost at 30hz, which probably indicates an f3 of 20hz or higher for the rumble filter...in other words, you shouldn't be able to bottom the SW12A with 350 watts, but you do have enough excursion to run the amp into clipping. Above 20hz, your excursion limited power handling is good for 500 watts except around 31hz, where it dips to 440ish.
Looking even deeper, I forgot,the SW12 is an 8ohm nominal driver. The simulated impedance curve only dips to a low of 7.8 ohms so you're getting 280 watts or less sustained out of the Senior...making it
highly unlikely you've bottomed the driver with that amp.
Standard questions. How did you calibrate your subs to your mains? What size room? What's the distance to your seat from the sub? How loud do you listen in terms of SPL or relative to a 75db/85db calibrated reference level?
In the end, output is about air displacement...a function of Xmax and Power. The SSi has more potential output and a decent looking response curve in that box, but you'll need more power than the Senior can provide. With a suitable rumble filter, that SSi in 2.4/19 will handle 1500 watts nicely for >111db from 20hz up at 1m ground plane. No idea if the CSS
PR can handle that kind of excursion. A suitable port would be too large to fit inside the box, not that it actually has to for proper function...SAF is generally kind of low with an outie port, though.
In short, a driver change alone is not going to move the needle in a meaningful way, IMO.
-Brent