If the source of my conscious choices was detectable by human scientific investigation, it would not be a conscious choice - just an unavoidable reaction driven by the laws of science (not by me).
Actually, unless you have evidence to the contrary, the source of your conscious choice is the brain for which there is ample evidence(e.g. when the brain dies, consciousness dies). Whereas all you have is an idea which you have agreed cannot be anything but an idea, because it is undetectable.
'Conscious choice' simply means that you are aware of the fact that you are choosing between two or more possibilities. It says nothing about how that choice is made and therefore there is no reason to think that it is not the product of 'unavoidable reaction(s)' especially as a) there is nothing to suggest other than that the brain makes these choices(your alternative is 'undetectable' remember). And b) even if your 'undetectable source' was found it would still logically have to have a deterministic process which controls it as you have rejected randomness, which is the only other alternative.
Finally, as far as we can tell, we are products of the laws of science, hence we must be driven by them, unless, of course, you can give some evidence that suggests something other than the laws of science have contributed to what you call 'me'.
It seems to me that you are not only batting on a sticky wicket, but you are stuck there in a quagmire of your own making.
