Wow - that's amazing, guys! Based on the isolation provided at 12:22 in the video above, I think it safe to say it's "organ only". And, the reediness evident in that isolated track does make me think "harmonium rather than Hammond". On the finished product, it sounds like the "highs" have been tweaked via EQ, but here it sounds more "flat" and "reedy". What was your source for the isolation?
I'm the author of those videos and the source for the organ audio there is from the SOT Pet Sounds box, which is essentially a haphazard dump of the multis. I think I used the vocal track from another track on there to pan the organ out and further isolate it, which is why it sounds a little phasey.
Here's another question related to "IKTAA" - Glen Campbell's banjo overdub appears twice in the song: during the bass harmonica solo, and again during the tag. Does anyone think that there's also a woodwind part on the same track as the banjo in the tag? To me, listening to the stereo mix, it kinda seems like a prominent clarinet line might be doubled on the same track as the banjo, but the separation isn't profound enough for me to tell for sure. The reason I suspect this is that both Glen and Steve Douglas were paid a full hour of overtime on that recording date, and they're the only two musicians who were (engineer Chuck Britz also was - but the other players only got a half-hour of OT)...Glen's extra half-hour of OT is obviously because he stayed behind after the others were dismissed and played that banjo overdub part. I hear no woodwind during the solo, but during the tag, not only do I hear the clarinets (and likely alto flutes) from the basic track, but as I said, possibly another clarinet on the banjo track, doubling the main clarinet part from the basic track. Anyone else hear that? Is it possible to isolate the banjo track during the tag?
The full banjo track can be heard in the far right channel on the SOT Pet Sounds box also on the track labeled "Take 12 Master Take". The first part of the song Glen can be heard tuning up and practicing. From what I can hear there's nothing else on that track but the banjo.