I have the same serial number plate on my TP-2. There is barely 3/8" of plastic below the serial number plate, and to make the 7-round magazine fit you would have to remove a half inch (4/8") of length.
Your best bet would be to try to find one of the older ones. And I would not trust an online sale -- I would have to verify the placement of the serial number.
Can you just mount the CT9 slide/barrel on a P9 frame?
I have a 23 year-old P9. I was able to mount its slide on a CT9 frame and on a TP9-2 frame. I did not try to fire it. It might be useful if you wanted to be able to press the gun against the target without pushing the slide out of battery.
I could not mount the TP-2 slide nor the CT9 slide on the P-9 frame. But if if someone has a newer P-9 or a CW-9 they might try it.
Experimenting further, I noticed that the thin metal floorplate of the MK-9 / PM-9 does not cover up as much of the magazine body as does the plastic floorplate that comes with CW9 / P-9 / CT9 / TP9 magazines.
So, if you replaced the magazine floor plate with the metal one (you can get them from Kahr), and cut 3/8" from the handle, it might work.
In fact, it probably will work, if you're willing to shave down a tiny bit from the bottom corner of the serial number shield.
I suppose that what's most important is that you can still read the number. And you might be able to shave a tiny bit of plastic even from under the corner of the serial number shield.
If you're worried about pricking your hand with that corner when you slam the magazine home, you might just add a tiny bit of material (e.g. epoxy paste) on the bottom of the floorplate to keep your flesh from pushing against the serial number shield corner.
So, yeah, you can probably make it work if you switch to using the metal floorplate. But there's no question if you can get your hands on an older model TP9 / CT9.
The difference in length of the magazines is half an inch -- more than the diameter of a cartridge. I suppose every increase in capacity adds to the weight of the rounds, which requires a stronger and longer spring, and maybe more room to hold the fully compacted spring. (But see my earlier comments.)