You hit right on it when you mention the point where you start believing the voice. That really is the fork in the road.
I take a couple of steps. First I recognize that inner voice and separate it from myself (a bit like AVRT). I acknowledge it and remind myself that even if the concern is a valid one, my current anxious state means that thinking about it won't be productive.
Then I mentally focus on my body and try to feel the anxiety as a physical sensation... noticing if my muscles are tense, if I have any points of tightness (often in my chest), if my heart rate is faster.
Then I try to disassociate those physical sensations from any kind of narrative in my mind. My chest isn't tight
because I don't have enough savings; my chest is just tight. Like my feet would be sore if I'd be walking all day.
And then I focus on my breath and try to breathe my way through the physical sensation.
Depending on how bad the anxiety is, this might work right away, or I might have to keep at it for a while. One important part is not to feel like I'm trying to "fix" the anxiety... that just causes more anxiety. Instead it's just allowing it to happen without adding fuel to it.
I bicycle, and I find my technique for long climbs is very similar. The hill is there and it's a certain size, and I have to get to the top. If I start getting upset about how hard it is to climb and how hot out it is and how I want to get to the top, I start pushing too hard on the pedals and tiring myself out in weird places. If I detach from wanting to get to the top and just focus on my breath and on the feeling of the climb, I get a better motion going and it tires me less.
I also find yoga a great way to practice. Here's a good article about how it helps:
Yoga: Changing The Brain's Stressful Habits | Psychology Today