Otherwise, it's pretty easy to construct a scenario with a ridiculous result that enables aurder spree that everyone could have predicted.
“It would have to be a fully-adversarial process with notice, judicial determination, appealable, and of limited duration.”
You quickly get to a situation where someone has to spend $1,000 to get a $800 gun back.
Existing red flag laws only meet one of your criteria - appealable.
While they may allow situations for notice to be given, there are emergency considerations where the only notice is a knock on your door.
All the laws also allow the police to make the claim of a subject's danger. That means if someone makes a call to them, even if that individual doesn't want to file a claim themselves, the police can take over.
For domestic cases, this typically occurs at night (drinking time) and guess what - the judge is at home.
The decision to allow a red flag seizure is usually made by a magistrate - the guy the works in lieu of a judge after hours. They rubber stamp anything a cop brings them.
Finally, since you have to prove yourself sane to even attempt to get your gun back (and good luck w/that), the duration is indeterminate and possibly for life.