My experience is not perfectly analogous to yours, since I struggle with chronic muscle tension. However, during meditation, it has often tended to get worse.
In my experience, tension - both mental and physical - comes from a controlling attitude, which is often invisible to us. Wishing it away, preferring it was not there, or deliberate efforts to make it go away seem to be temporarily effective, at best, and often counterproductive.
My best suggestion for counteracting a controlling mind is cultivating a good sense of non-self (not me, not mine) with regard to all phenomena, including (perhaps especially) the mind.
To aid this effort, I have one particularly effective technique. It works for me personally; your mileage may vary.
Consider how, when you look at the stars, you’re seeing how the stars were millions of years ago, when the light left them and only a moment ago met your retina. Everything you’re aware of “right now” is, in fact, old news. All light and sounds take time to reach your retina and your ears. Sensory impulses take time to reach your brain, and more time to be integrated into an image/sound/idea of what just happened. Whatever you’re aware of isn’t happening anymore. Everything you experience, by time you’re aware of it, is a reflection of how things were in the past, not how they are right now. They’re phenomena.
So to get a good sense of not-self going, I keep constantly in mind that everything I’m experiencing “now” is already gone, the phenomena represents prior causes and conditions (conditionality). When I watch impressions of the body in this way, feelings in this way, and especially my mind in this way, I get a good sense of not-self.
I say “especially the mind”, because it is the mind that clings to other phenomena (such as unpleasant bodily tension), and the mind that suffers as a result. The conditionality of all phenomena, means I cannot control the “current” state of the mind (by time I am aware, it is too late). If I cannot control the mind, trying to only creates more tension.
So instead, I try to watch the mind knowing “that is how it was a moment ago”. If the mind I’m aware of is an uncontrollable experience of prior conditions, is not me or mine, what is there to control? So I can approach the mind and its experience with genuine self-less metta. I can’t control it, so the best I can do is to make helpful suggestions based on my observations. So I just ask “what was it clinging to a moment ago? what still feels like it’s me or mine? body? feelings? thoughts? what could it release?”
Just making these observations in the present seems to give the mind the knowledge of what it needs to do to fix most of its problems down the line. For example, reminding the mind that feeling is an empty phenomena, already gone, uncontrollable, not worth clinging to, seems to help it. But only if done with compassion and detachment, knowing that the mind we experience is also not-self, past and gone, and can’t be compelled to do anything.
Just my experience - I hope it helps