Any chance you could borrow another known good MAF? Was the one you fitted new or used?
Sorry, just trying to eliminate things.
Just a long shot but is it worth checking the idle control valve. Could try cleaning it and check the sealing? Seems like you’ve checked everything else.
Hi
yes, the MAF is new, so i’m reasonably (but not totally - as it’s not a Mazda part) confident that it’s ok.
the Long Term Fuel Trim stays at 0 (the short term jumps around), which i think points to the fact that the o2 sensors are happy with what they’re seeing so the MAF and O2 sensors all seem to be aligned (this is based on limited understanding!). although, i haven’t really driven it long enough in closed loop to be totally sure.
i’ve taken a superficial look at the earth points and they all look clean, ie no rust, nice solid cables - the car is rust free. i’m going to earth the engine directly to the battery - and take it out for a spin (doesn’t help that the battery is in the boot 
). i was thinking of connecting the jump lead to engine hoist point - is this a good place?
wrt the idling control valve - i’ve purposely not messed with anything to do with the idling as i think the stalling is related to the slight misfiring at low/mid revs - so i was working on the assumption that it wasn’t an idling specific issue, and the poor idling was more of a symptom - but i could be wrong.
Quick update: i’ve revisited the MAF. i ordered the part from MicksGarage.com entering my vehicle registration, so i was reasonably confident that i had the right part, which was the ‘Air Mass Sensor Cambiare VE700268’
i called MicksGarage today and asked them whehter this was directly compatible with Mazda FS1E (suitable for my exact model, 2004) part, to which they said ‘yes’.
However, when i doublechecked as to whther it was also comaptable with the Mazda FP39 part, they said ‘no’ (which was good) - BUT it was compataible with the Mazda FP3913215 part! Which worried me, as earlier in this thread it was mentioned that i needed a FS1E equivalent part, and i could not use a FP39 part (i’m assuming that FP3913215 is a ‘FP39’ part).
Looking online the Cambiare VE700268 only seems to be equivalent to the Mazda FP3913215 - so i’m not sure why MicksGarage would think it to be suitable for my year of car.
So the bottomline is, i think i have the wrong MAF. Am i right?
Does anyone know what happens if you have the wrong MAF version, ie a FP39 instead of the FS1E? Would it give the symptons that i’m now seeing?
I have not actually tested the theory Steve but as far as I know they are not interchangeable.
Would imagine this has something to do with advanced ECU control and onboard diagnostics on the later car.
Ok, i borrowed a FS1E MAF from a friend - fitted it and the car now runs perfectly!
so the issue was initially a faulty MAF and then an incorrect FP39 MAF fitted.
thankyou everybody for all your help - it was really appreciated!
Thanks - you were right! (see reply above) 
We had the same issue and my son adjusted the spring inside the MAF and that fixed it.
Glad to hear you’ve got it sorted.