Aside from many of the points already raised, and without having gone over every last detail of the process:
I note that, in the case of an emergency removal, the reinstatement process is concluded at Discovery.4.1.2 which reads, emphasis original:
If an Emergency Removal took place and it's since been explained, and no further action is needed, moderator access can be restored, and any appropriate security measures should be communicated. The process is concluded here.
Key word: "can".
I fully understand that there may be times when moderator access needs to be revoked on short notice to prevent further immediate harm to a site or the network as a whole. Such scenarios, I feel it goes without really saying, should be exceedingly rare. What looks like a compromised account certainly can be one example of such a scenario.
However, any emergency removal of moderator powers must explicitly be with the full understanding and recognition by all parties involved that such removal of powers is strictly temporary and done only in order to prevent further immediate harm.
The moderator who had their powers removed under this emergency authority should then immediately be contacted, presented with the evidence, and given the opportunity to explain what happened, or go through the full review process as if their moderator powers had not been removed in the first place (in other words, the review would have to find evidence requiring the moderator to be removed; it would not have to find evidence allowing the moderator to be reinstated). I realize that collecting the evidence in a reasonably presentable form could take a short while, but I can see no plausible reason why such a contact, including presenting the evidence, shouldn't be possible within, say, 24 hours.
If, and only if, any of (a) communication, (b) further review of the events that prompted the emergency removal, or (c) the prolonged lack of a response, indicates both that the activity was actively malicious and on the part of the moderator themselves, should moderator access not be restored. In all other cases of emergency removals, moderator access should be restored by default once the situation has been resolved through mutual communication.
This does not preclude the possibility of communicating appropriate security measures as part of, or as a precondition for, restoration of moderator access. It also does not, for example in cases of inappropriate behavior, preclude the possibility of communicating a clear and specific warning to the moderator.
As an example, nothing in this is to be taken as preventing such communications from concluding by saying something like: "Make sure you immediately change the password on your account to a secure one. We will be able to restore your diamond once we see that your password has been changed. If your account is used again in the future to vandalize content, as happened with the posts previously referenced, we will have to go through the Moderator Conduct Review Process and possibly permanently remove your moderator access."