Thanks to mbraortns on this thread for their advice. This is what I’ve done to be able to fly without the white dot on Xbox using a controller (in May 2023)…
Starting off with the default controller settings, firstly set “Toggle cockpit free look” to be left d-pad.
Unmap “Toggle cockpit view freelook (hold)” from LB to be nothing.
Next, set “Cockpit camera slide back (lockable)” to LB+right stick back.
Then do the same for “cockpit camera slide right/left/forward”, using LB and the corresponding direction on the right stick.
Please note, after doing this, you will only be able to move around the cockpit once free look has been toggled (i.e., once the white dot has gone). Alternatively, you can map “Translate cockpit view right/left/etc”, to the same button combinations (ie LB+right stick right/left/etc). Using this, you can move around in either views (i.e., with or without white dot). But you can also move the camera outside of the cockpit. Anyway, too much info, feel free to ignore this paragraph!
Next I unmapped “cockpit camera height inc (lockable)” that was using RT, and also “cockpit camera heigh dec (lockable)” that was using LT. I don’t find these useful anyway. Or to keep them, remap it to something unused. But you need to change it, because otherwise you’ll start using the rudder unintentionally.
That’s pretty much it. Make sure “cursor toggle” is still set as a press of the left stick (it already is by default). I also mapped parking break as A+B (as it used to be left on the d-pad, which is now in use).
So, now when you go for a flight, pressing left on the d-pad removes the white dot. Doing it again brings it back.
Hope this helps. Let’s hope “Toggle cockpit free look” isn’t removed next, or they just give an option for people to remove the white dot in the options!