Shirley is Maiden's engineer, not producer. He did his job very well, as he does. He doesn't have a say (for 20+ years, since day 1) in sound or arrangements. By his own addmission, he's there to "mic up guitarist's cabinets" and let them be themselves, he tweaked drum sound only in BNW and has opinion that if Nicko tunes his drums correctly they're going to sound good.
As an engineer he's there to capture their sound.
Steve Harris is chiefly Maiden's producer but on this album we can see that Smith has got some leverage when it comes to his tracks.
If you recall the interviews, it's Steve that wanted guitarists to play specific kind of solos and worked with them on it. That's absolutely the job that producer does.
Maiden sounds the way Maiden wants to sound, Shirley is just the means to get that on tape. If you have problem with the way Maiden sounds it's down to Harris in most cases.
Maiden never had a Bob Rock - certainly not that down in career when Metallica hired him.
He totally changed the way band does things and introduced a 'big name producer' to the band (and to the genre I'd say).
Birch was more of a big name engineer. Apart from the TNOTB scream story with Dickinson, and Murray/Smith saying he gave them a hard time with solo recording (they say that about Shirley too), where are his big name producer interventions to the albums?
He wasn't the type and eventually Maiden found a replacement in the same kind of a professional.
Maiden is in essence self produced since the mid 80s.
The things you need to look for if you like 80s but dislike newer stuff. The 80s haven't got a thick guitar sound and they haven't got an orchestration going and the drums usually sound like shit. I think albums such as Piece of Mind or Powerslave have been recorded very organically, L-R separation of guitars, multitrack here and there, very wide sound. I think album such as AMOLAD has been done the same. The difference in sound is the difference in amps, drums, instruments and arrangements, nothing more to it. You will find that the greatest difference between typical 'hard rock' amp sound is between early 80s and early 90s. The early 90s amps are what we consider 'modern metal sound' today.
The definition of Statocaster into Marshall remains but the sound is different. Back in 70s/early 80s, those were low gain pups and low gain amps. After mid 80s those were high gain hums and high gain amps.