Is it possible to overcome this annoying habit of what I assume is the computer cutting off the fuel under WOT 3rd, 4th. (never got to 5th yet)?
When this happens it is like turning off the key for an instant and if I continue at WOT the engine keeps cutting in and out. If I back off on the throttle slightly it comes back and I can sometimes nurse it to max RPM. Too be truthful I've not always noticed if I was initially over 12psi but it even does it at 10psi. It doesn't happen all the time but about 90% .
(Fuel Filter?)

 

Do you have the stock ECU or an aftermarket? My PFS PMC had the max boost fuel cutoff values entered incorrectly. After putting in the correct values in menu 900, the problem went away. It can be more than an annoying problem. The first time it happened to me, I was passing a car on a two lane road with traffic approaching when the engine died. Fortunately, I had enough momentum built up to sort of coast past the car and get back in the right lane.
If you have the stock ECU and a lot of miles on the car, you might start, as you suggested, checking fuel filter, pressure, etc. If you can find a reliable Mazda mechanic, they can check your ECU settings for the max boost pressure setting for the fuel cut-off.
Ron A. 93 VR Touring, 90 BR GTUs.