You're right that there are no easy answers, especially for the mentally ill who may not be treatable. [Note: I come from NZ, so the perspective of a largely state-run health system].
I think that humane mental institutions would be a much better alternative to prison or surgical intervention.
A lot of people were locked up in mental institutions right up until the late 80s, early 90s. Often, people who should not have really been in them. I know people who were seriously fried by drugs administered largely to induce docility, and the brutal ECT of 50s-70s.
There were some serious problems with the way these institutions were run which were very difficult to fix. The pendulum has swung towards community care. In NZ at least, most of the mental hospitals have closed. The mentally ill were flooded back into the community. To be fair, the problems with the system were so severe that this was not an entirely bad outcome. Many have done well in the community.
From here we can divide the mentally ill into two classes: those who manage to function in the community, and those who end up in prison or dead. Sometimes it's the degree of social support they have which makes the difference, while some simply cannot be treated.
I think the pendulum needs to swing the other way a little. We need to identify the truly dangerous and incurable and care for them in humane environments before they hurt themselves or others.
Identifying when this needs to be done and ensuring the system works properly is obviously an incredibly difficult problem. Essentially you will be locking people up based on psychiatric diagnoses for things they haven't done yet. However in the current scheme of things even clear pleas from family members for intervention are ignored.
As an aside, I'd like to point out that you're proposing to take people who might be psychotic or schizophrenic, and implant remote control devices in them.