Great questions! First of all, let me clarify that ligaments can and do stretch and get longer. That is quite okay and necessary. However, they normally do not stretch as much as muscles do. I am not so sure that stressing ligaments or fascia do not increase their length, but it definitely can increase their strength. I think the confusion may arise over whether we are talking short term or very long term. It takes a long time to remodel fascia and collagen. Muscles can change after a few weeks of work, but ligaments can also change but only if you keep at it over months and years. The intention in our yin yoga postures is not to permanently elongate fascia during one practice, but over time the changes can occur.
Your point about muscles being relaxed versus muscles being warmed acting the same with respect to ligaments is very cogent. I agree! I have not really talked about this, but there is a benefit in both ways because we have both parallel and series tissues attached to muscles. If we want to stress the ligaments, keeping the muscles cold does a better job, but also, as you surmise, keeping the muscles engaged will also help more of the stress reach the ligaments. So, here is a case where it may be okay to engage the muscles! But, we don't want to keep muscles engage for 5 minutes or longer: that is not a great way to exercise muscles; better to let them relax but stay cool. (It is ironic that many teachers criticize Yin Yoga because it may stress the ligaments but then they advise their students to engage the muscles to avoid this. It actually creates more tension on the ligaments!)
Another benefit to relaxing muscles is the effect, not on the ligaments which is a serial tissue to the muscle, but to the parallel tissues of the joint capsule. When the muscles are engaged, they shrink the joint capsule preventing traction from occurring. If we want to target the joint capsule, we do need to relax the muscles. The forefinger experiment illustrates this: stick out your right forefinger and stiffen it. While the muscles are engaged to stiffen the finger, try to bend it. You can't. Because the muscles are engaged, the joint won't move. But, now relax the muscle and try to bend it. Now you can move the joint to its end range of motion and stress the joint capsule. (I think I may need to write an article about this!) When we practice with relaxed muscles we can affect the joint capsules better because they are in parallel to the muscles.
Yes, you can say that Yin Yoga will elongate the muscles: everyone can feel that! Come into Straddle with legs wide: most people feel a lovely stress in the groins (the adductors) which are muscles being stretched. Yin Yoga does affect the muscles and we should never deny that! It won't strengthen the muscles, you need resistance training for that, but it will lengthen the muscles due to the fact that the muscles are 30% fascia! Whether Yin Yoga elongates the muscles more that the tendons and ligaments you can't say, because it depends upon which muscles, tendons and ligaments. They are not all the same. The ligamentum flavum along the spine is very stretchy and will elongate as much or more than the back muscles in a forward fold.
Finally, how to stress ligament without stretching them? I don't know. Why would you want that? Any tissue under load will change shape. Ligaments are designed to stretch, just not very much, usually. Most will only stretch 5~10% and that's fine. But others, like the ligamentum flavum can stretch 60% or more. Here is my article on It is Okay to Stretch Ligaments