The Geiger counter is measuring a phenomena that is random, but producing a ‘click’ once that random phenomena occurs is fundamentally deterministic. People who believe indeterminacy supports free will do so because they believe their will gets to ‘select’ a certain path, so the ‘randomness’ comes from their free will. So a computer with a Geiger counter doesn’t have free will because although it is measuring a random process, it doesn’t affect the process as it does so.
People who do as you describe are appealing not to quantum physics itself but rather to the mystic of quantum physics.. quantum woo. 'Quantum' is a word they throw around to give a veneer of science to their assertions, but there is nothing in the science of quantum physics that supports the notion of free will being expressed through the control of stochastic quantum phenomena like radioactive decay. People who appeal to quantum physics in this way are like people who appeal to magnetism to explain why crystals and pyramids have healing properties; there is nothing in the physics of magnetism that supports such claims, but magnets are mysterious enough to laypeople that "because magnets" is enough to impress the credulous. They're using words associated with science to imbue their ideas with some of science's credibility.
To simplify, the fundamental question of human free will is “why does it feel like we can freely make decisions?” And quantum theory can provide an ‘out’ that it feels this way because our decisions change the results of otherwise seemingly stochastic processes. If the universe isn’t choosing the outcome deterministically, maybe our consciousness is.
Assuming you believe in determinism, what is your explanation for stochastic processes? My naive view is that you either need faith that we will discover a deterministic explanation for the perceived randomness, or you need to drop your assumption of a deterministic universe. If you drop that assumption, why do you still reject the possibility of free will?
I’m not saying you’re wrong, but I don’t think your chain of reasoning makes sense.
Edit: I decided to have a look for more knowledgeable opinions than mine, and found a Nobel laureate who thinks there is a possibility https://en.m.wikipedia.org/wiki/Orchestrated_objective_reduc... . As far as I can tell none of his theory has been falsified.