Ugh.
The EEA might be best for everyone, because it is a canned deal, no need to invent anything.
Then you accept total freedom of movement, as it is quite explicitly a part of the deal.
If you don't want freedom of movement, then you have to invent something.
Again, Art. 112 is a
temporary safeguard in respect to
unexpected major
difficulties (full disclosure: this part is interpretation). Three things that aren't the case in the scenario you are advocating.
And Art. 112 is not explicitly about freedom of movement, unlike those other Articles I linked earlier.
Invoking a safeguard once in EEA does not mean you don't intend to fulfill the EEA agreement - to the contrary, you are acting strictly according to it. Entering the EEA with an intent to invoke a safeguard similarly does not mean you are entering with an intent to not fulfill the EEA agreement - again, invoking a safeguard is completely within the agreement, you are fulfilling it. You are equating EEA with "EEA without the safeguards". You can't do that. There is no bad faith here.
Invoking a safeguard directly after having signed a deal means you don't agree with one clause of the deal at the moment of your signature.
Again, however you spin it, that is bad faith.
In the case of Lichtenstein for example, it wasn't bad faith, because for all intent and purposes, it did intend to accept free movement (and did do so for a while) at the moment of the signature.
Changing circumstances made them turn tail on that, to which the EEA agreed to considering the circumstances.
Art. 112 doesn't explicitly say you have a right to establish quotas unilaterally (or even multilaterally). If it did, it would make the whole treaty moot, as it contradicts many major Articles of the treaty.
What you
can do to make this not a bad faith case, is explicitly and formally (i.e. included in the treaty) inform your intent to use Art. 112 in that way as soon as you enter. But again, then we're back to our other point: why the hell should the EEA sign that?
No, I don't want to advocate that the UK tries to enter something that is similar to EEA but with an additional provision equivalent to the safeguard. If we could have negotiations in some parallel universe where they would take however many years of that universe's time and only a month or a year of our time, it would have been different - but then I'd have advocated for negotiating the entire exit at once (and yes, that would include limits on freedom of movement). But we have what we have - both the EU and the UK, and the safeguard clause works. If it doesn't work for the EU, they will say so.
Remember a few weeks ago when everybody was saying that UK had a bad negotiation position?
Well that is why.
I know it doesn't fit your expectation, but the EEA treaty is what it is, and it does include unconditional freedom of movement, and no, Art. 112 can and would be overturned if it were used in the manner described (in addition to making your negotiating position even worse).