I can only describe my own experience. Which starts from a different type of horse. Having degeneration in my lower spine means I need to ride a narrow horse. Cobs are ruled out but much depends on the shape of the top of the horse's back, a broad flat back is worse of all.
I ride in an open saddle. You describe sliding forward on downward transition - it might be possible to work out why? Because bareback one should be able to sit securely on transitions even with no saddle to hold one in place. I learned to ride in my 60s and came into the hands of a RDA trained classical RI who gives lunge lessons teaching one how to sit on a horse and how to adjust one's seat for the best balance. It sounds as if you are depending on the saddle for that?
But you switched to a saddle that had more structure too it and knee rolls and my answer to that is yes - I suffered. When my share's saddle went to be reflocked they lent me the best saddle on the yard -a dressage saddle that held me in place. I hacked in it once only and it crippled me. Just as you describe.
One of the benefits of riding for an older person or in RDA is that riding involves constant tiny adjustments of one's muscles in order to hold one well balanced on top of a moving animal. If one rides in a confining saddle that restricts ones movements, one is bound to move less and in cold weather will stiffen up more. It is always hard to dismount in cold weather and I was taught to stand up in the stirrups a few times and also wriggle my toes before getting off the horse.
As for going long distance - I have never done more than 2 hours without a break and I have usually given my body a rest but not cantering long distances on two consecutive days.
So riding into old age is a compromise.
In the picture you post, the position you are in is with your head (the heaviest part of your body) well forward as if you are bound to tip forward. Plus you seem to have a seat saver that will make the horse wider.
Dont get me wrong. I have not been taught to ride in a picture book position with head hips and heels aligned on the vertical. But I have been taught to sit and feel the horse through my seat with the weight on my two hip bones. And then when one isnt sitting, in rising trot to roll my hips forward. In forward seat I was taught to fold my body a bit like an ironing board. The weight of one's head going forward must be balanced by one's bum going backwards.
I have a big fleshy back side and I need a saddle with room for me to sit on it. The saddle in your picture doesnt look if you have room to sit flat on it in front of the cantle. And if you are sitting on a sloping surface, that slope of the saddle will slide you forward on downward transitions. In the USA Western especially riding in mountains, the saddle fits the seat size of the rider rather than the horse.
If you learned to ride as a kid, you didnt need these adult verbal instructions. So tho your question is whether it is the saddle or old age? I suggest that it is a bit of both.
I would also add a note, that I have not often ridden in a treeless saddle. I ride bareback or in a treed saddle and the tree raises one off the back of the horse, thus probably reducing the spread required between the rider's hips. And a further note that I am a RS rider so have ridden in dozens of GP saddles. It is the knee rolls that are the problem.,