I tried to sum up my problem in the title, but here is a more detailed version:

I recently swapped wheels from my newer bike to this one. Both wheelsets are Mavic Ksyrium SL, although I am trying to put a 2006 Mavic 10-speed wheel in place of a 2003 Mavic 9-speed wheel, using the correct 9-speed cassette I've been using, of course. To start, I simply transplanted my 9-speed cassette onto the new wheel, and it mounted up fine with no spacer behind the cassette. I was surprised to see that the rear derailleur was no longer in line, though. I had to adjust the limit screws a bit to get it to look right in the stand, and tighten the cable tension via barrel adjuster to get it to shift reliably again.

Everything works great when single click shifting or sweeping the lever further for a double click shift, and it works anywhere on the cassette. A 3-click sweep even works for all but the 4th cog, when trying to end up on the largest cog at the third click. The chain will shift onto the cog, but the shifter won't click a third time (unless I place an entirely unreasonable amount of force on the lever), and as soon as I release it, the chain jumps back down to the second cog.

How can every other shift be perfectly fine, verified on a ride today after the swap, but not that one instance of trying to 3-click into my largest cog? This is the same cassette I've been running for a while. Neither the cassette or chain are worn much, as I replace the chain every 2000 miles or 2 months, whichever comes first. The cassette isn't some ridiculous climbing one with huge gears either- it is a fairly standard 12-25 Shimano Ultegra 9-speed cassette, and this bike has also worked flawlessly in the past with 12-23 and 12-27 cassettes.

This issue is really blowing my mind right now, and it is frustrating me more than it probably should. Any ideas?