gm/Id is for linear interests IMO, and slew rate is just the output current
you can get with a hard-steered front end (with some influence of the
gate drive "stiffness" against Miller capacitance once it begins to move).
I think you should step back and assess appropriateness of the method
to the task.
But I've never used gm/Id in any of the op amps, error amps, reference
buffers etc. that I've designed, so maybe there's some use for it in this.
If so I'm sure your assessment will turn it up.
In my observation a lot of people are really keen to discuss gm/Id and
it seems to be viewed as The One True Religion by some (professors,
for sure). But professors get to pick the problems they have to solve.
And they loves them some closed form algebra just when you were
wanting to get on with transistor-slappin'. Doesn't mean they are good
(or competent, even) IC designers. In fact the smart money would
follow the money and bet against it. So listen and learn, but reserve
your faith.