Yep. I wouldn't be happy, but then again I wouldn't be happy if they searched my home and found the bodies, but I would submit.
The 5th amendment is about government over-reach. If you assume the government is only looking for dead-bodies, and the only people hiding them are criminals then its easy to get swept up behind the idea that anything the government can get a warrant for is fair game. Only criminals will be punished.
But there should be some limits. Even if that means some times some criminals don't get caught, because the alternative leads to a grossly oppressive state.
There are limits. Those are defined by the constitution, and include the warrant system as further defined by the courts. Yes, some of these technologies give interesting edge cases, but I don't think any of them require fundamental changes to the legal framework.
As you stated, the reason the limitations on police powers of investigation are there is to prevent overreaching and false convictions. Retrieving physical evidence after a properly executed warrant doesn't seem like an issue to me, and I have absolutely no fear that anyone is going to be able to read people's minds in anything like the lifetime of my great-grandchildren.
"We found DNA... no full match in the system, but we know he's related to this guy who was arrested once for shoplifting -- he wasn't the guy, but they took his dna and now its in the system... but I digress... they share a grandparent... so its his cousin. We checked birth records ... he has 2, one lives in this city... so we're picking him up now..."
That's effectively being in a DNA database for not being particularly closely related to a guy who didn't do anything wrong.
You are choosing poor examples. The various constitutional amendments are designed to prevent abuses that harm people, except in the type of harm that is defined as putting the guilty in jail. We don't compel self-incrimination because it leads to abuses that harm many innocent people, and is not particularly effective at catching the guilty. If you want to argue against you are going to have to show that your hypothetical database and the described police procedure has much greater societal harm than this one.
A better reason for limiting these types of databases is the problem of false positives. If you database is large enough, even with 99.99 percent accuracy (a failure rate of 0.01%) we would have lots of innocent people being flagged in these types of searches. This type of thing already happens for fingerprint analysis, and while genetic comparisons should in principle allow us to confidently pick out any individual in the world (except for clones I suppose), in practice DNA evidence is only comparing a very tiny part of the DNA, and errors in application which can never all be eliminated, so it will never be perfectly accurate.
Compelling people to tell your their password in my mind is a problem - there are lots of ways that an innocent person could be harmed by that. Compelling people to give up their implanted devices with a proper warrant is not as big of a problem in my mind. If warrants are being issued for individuals without good "probable cause", that is a problem. If extracting the evidence is onerous or dangerous or painful, then there should be a higher barrier to getting the warrant. If there are increased expectations of privacy for example lawyers or times spent at home, then perhaps there need to be guidelines on how the implant data is analyzed, but all of these types of issues are currently considered under the existing frameworks.
My thesis is that cyborgs do have the same right to privacy as anyone else, and that no new laws need be drafted specifically for people with implants. To motivate any such laws, I think we need to demonstrate that the current practice has negative consequences to society or innocent individuals. Making it easier to catch criminals is not, by itself, a reason to reject a new practice.