Cloud has 202 Attack, 220 Defence, 68 Magic, and 145 Magic Defence - Front Row
Aerith has 84 Attack, 198 Defence, 179 Magic, and 174 Magic Defence - Back Row
Cid has 242 Attack, 146 Defence, 49 Magic, and 116 Magic Defence - Front Row
I kept the materia, equipment, etc. the same and went into the battle to check damage. I took some screens to show damage difference between the three characters from various physical attacks. First we have W-Machine Gun against the party with barrier up:
https://imgur.com/a/gADH5Cid took the most damage at 919, which would double to 1800 or so if Barrier wasn't up. Cloud's defence seems much tankier by comparison, taking 300 (600 without barrier). If Crits land then I think this damage would multiply up by 2x; so 3600 max for Cid (not counting variance so maybe as high as 4000 max with no mitigation if a crit lands on him). Next is the single-target Punch:
https://imgur.com/a/q2NjzThis seems roughly as strong as Machine Gun, dealing 550 damage to Aeris compared to 500. I think its base power is 40 vs. Machine Gun's 32. Next is the HEAT Missile:
https://imgur.com/a/rMMiuCloud took the least damage against Machine Gun but he takes a lot more damage from this attack. It's likely this would deal exponentially more damage against Cid who has about 80 less defence (this is equal to 160 less defence compared to vanilla stats).
As for inflicting damage, I was dealing about 10-20 against Clod's main body while the Jamar Armour was intact. The Armour took the expected amount of damage, about 500-1000 from physicals, 3700 or so from Aeris' Hydro spell. Once it died, the boss' defence fell and took similar amounts of damage from that point onward.
I'll need to know how much damage each of your party members takes individually from a non-critical Machine Gun to determine if the numbers match up. I've posted some strategy stuff below as well for prepping the fight.
For optimisation, it'd be a good shout to give Cid and Cloud some Elemental Materia into their weapon combo'd with Lightning or Water for 2x damage on their physicals. If you don't mind burning an Elixir or Turbo Ether during the fight then Hydro can be buffed up using MP Turbo over MP Absorb. Cid should prob drop Comet and just focus on physicals, you've a spare Added Cut in there that could go onto his Steal/Mug for a makeshift 2x-Cut instead of Command Counter.
Fury seemed to work OK, but it caused Hydro to miss a few times and I only got one set of Limit Breaks during the fight for it.
For opening the fight, I had Aeris start with Regen, Cid use Wall on himself, and Cloud used Barrier on himself; we went after the Jamar Armour first (more or less have to due to the defence on the main body). You could maybe swap the two Barrier Materia that Cloud and Cid have so that you can make use of Wall + All instead of Barrier + All as Clod has some powerful magical attacks to watch out for later in the fight like Beam Cannon.
If status ailments are causing trouble then bring in your Added Effect Materia and attach them to the status magic that is proving most problematic in the fight. Paralysis unfortunately can't be covered with Added Effect due to a limitation with Materia flags but you could sacrifice the accessory slot for Jem Ring to block that status on someone with access to Heal Materia so they can always be available to use Esuna; that or Remedy/Soft will heal Paralysis as well.