* Remember that turning on a transistor causes reduced drain-source voltage across it.
Simultaneously it sends greater current through neighboring components thus raising voltage across them.
* The Gilbert cell multiplies two signals. These need to ride a DC component in order to bias the transistors properly (including level 1, level 2, and the bottommost tail transistor).
* It's a complex circuit. I imagine a big challenge is to find a good operating point.
You may find it's crucial to operate all transistors in a linear region. Or instead you may need to operate certain transistors near their threshold of turn-On & turn-Off.
* Headroom seems to be only a minor factor to consider. There's numerous adjustments needed before the circuit works properly. Eventually it might come out that each level operates within a range of voltage, or within a percentage of supply voltage. Can these be determined ahead of time? I believe the circuit is too complex to predict ahead of time.