All joint movements have two sets of muscles, the sets are on the opposite sides of each joint. To make the joint move one way you tighten one muscle set and relax the opposite set, and to make the joint move the opposite way you swap the sets of muscles which are tightened and relaxed.
Todays Google search on spasticity brings back an answer from the American Association of Neurological Surgeons, which I have cut, pasted and trimmed: https://www.aans.org/Patients/Neurosurgical-Conditions-and-Treatments/Spasticity
Spasticity is a condition in which muscles stiffen or tighten, preventing normal fluid movement. The muscles remain contracted and resist being stretched, thus affecting movement. In the elbow example, if your biceps become spastic, then they remain contracted, which means that straightening your elbow becomes more difficult - the triceps have to do the usual work of moving your forearm and the additional work of fighting against the spastic biceps. If both sets of muscles are more spastic then it becomes more difficult to move the elbow in either direction - each muscle has to do its usual work, fight against the spasticity in the opposite muscle, and its own spasticity makes it difficult to move itself.
Muscle cells which are spastic become shorter and stiffer than similar cells not affected by spasticity. (ref: https://onlinelibrary.wiley.com/doi/abs/10.1002/mus.10247). The muscles themselves become physically shorter the more spastic they become. The opposite is also true, muscles that are stretched regularly are longer than those which are not. (This physically shorter/longer muscle point was the key thing I remembered from my physio discussion as the basis of this post)
The purpose of stretching is to help reverse the shortening of the muscle cells. There are plenty of websites offering similar opinions that stretching is beneficial for muscles (although equally there are studies saying that it is difficult to draw firm conclusions on this front). The key point is that if your HSP is such that you are less able or unable to operate the muscles, you can still bend the joint by other means (perhaps with help). By stretching the muscles regularly you can either prevent the muscle from becoming any shorter or reverse some of the shortening that has already occurred. This is one of of the areas where the HSP mantle: 'use it or lose it' comes from.
Doing a set of stretches will not change the signals which get fed up and down the spine, they will just change how easy it is for the muscle to move in response to the signals which are received from the brain. (Note - I wonder if the nerve signals from the muscles back to the brain may travel more easily, because the 'intended muscle position reached' signal may be stronger. A question for another day!)
From my perspective, I can still move all of my joints, although I cannot move some joints as far or as easily as I used to. The work that I did with my physio was to look at which muscles were becoming spastic, and to look at stretches to keep those muscles as long as possible. You can see the stretches that I was doing a few years ago here: https://hspjourney.blogspot.com/2018/04/stretching-routine.html. I have added a few more since then, and at some point I'll do an update post with the new ones.
As we know with HSP the spasticity in our muscles changes slowly as the nerves degrade slowly over time. Similarly, it takes time for the cells in muscles to grow as a result of regular stretching. The most difficult thing is trying to work out if you are getting any benefit from stretches or not. You are mentally trying to balance the speed of your HSP degradation against the slow speed of any gains in muscle length which you are making. So, it might be that you can detect the benefits of your stretches at other times by noticing, for example, that sitting at rest feels more easy than it did before.
My approach since I started doing my stretches has been to adapt those stretches to include muscles which I notice are becoming more stiff. My key areas of observation are; how difficult I find exercises at Pilates, how easy I can reach for things, how easy I can put my socks on/cut my toenails, how easy it is to use the stairs, how long it takes me to feel uncomfortable sitting down, and so on. I am still doing all of the stretches which are shown on that stretches page, and I have just added a few more in. I now do one set of stretches each day, which usually lasts between 15 and 20 minutes. Essentially I have become my own physiotherapist!