Hi,
Headroom has nothing to do with bandwidth! Looks like you don't understand fundamental trade-off in amplifiers design. I would recommend to read some basic books. For example, "Analog Design Essential" by W. Sansen.

If the amplifier designed properly (questionable? maybe), unity-gain-bandwidth product is defined by the compensation capacitor and and the tail current of the differential pair. So, increasing tail current or decreasing compensation capacitor improves UGBWP. To keep the same PM you have to increase the quiescent current of the output stage. I assume, you cannot decrease a load cap. Therefore, increasing BW leads to a larger current consumption.

Of course, my description is too optimistic since you have already a very high bandwidth. Various small parasitic poles at different nods can affect frequency response of an amplifier. So, more design efforts will be needed.

Replace current sources M20 and M21 with resistors and setup the cascode bias accordingly with mirrored a device and resistor. This will greatly reduce the capacitance on their nodes, at the expense of DC gain, possibly. Increase the lengths of most devices and eliminate their m multipliers. This will reduce their parasitics. Regarding headroom and bandwidth. Yes they do interact. If a reduced output voltage swing could be tolerated, then a push/pull source follower could be added, with the 2nd gain stage then greatly reduced in size, reducing its capacitance loading. The modified topology might well allow for higher bandwidth. Do you actually need a class B output?