Thanks again for all the replies.
If you have intense pain you stop immediately. Nothing helps like a break.
Yes, but two problems: (1) "intense" is subjective--if a doctor said there was nothing wrong, I would be inclined to think I just need to try to force myself lower and get over the pain (maybe I'm just weak); (2) whatever else might be wrong, there is underlying inflexibility in the knee, which needs to get stretched out in order to do seiza properly, so I can't just stop training for every discomfort.
Well, arguably that's true, but:
(1)Yes, "intense" is subjective, but that doesn't mean it should be ignored. It's telling you something; the trick is to figure out what the thing is. It's more nuanced than the simplistic extremes of, "If it hurts, stop" and "Pain is weakness leaving the body, RAWR!" Personally, I like to use the word "discomfort" rather than "pain": the latter has baggage, and people tend to ignore feelings of discomfort that are alerting them of problems because they feel they don't deserve the label of "pain".
The average sedentary person avoids discomfort and does whatever they can to alleviate it -- they don't have much experience in enduring it. Some discomfort should be endured, and some should be cured. It's knowing which is which that's the tricky part. Note that "endure" is not the same as "ignore". Any discomfort you feel is telling you something. Don't ignore it; do make an intelligent decision about whether to endure it.
(2)Inflexibility may be part of the problem, but from what I know of stretching and flexibility, if you're feeling intense discomfort, you're not improving flexibility. In other words, for you, right now, the action of sitting in seiza is not helping with whatever flexibility issues you have.
One thing that my sensei recommends (never tried it myself) is to spend some time sitting in seiza at home, but supported by a cushion such as a zafu or maybe a folded-over pillow. This may be helpful for you -- but not if you do it to the point of intense discomfort.