RNGesus is not on your side. Flamethrowers/gunners are relatively common on the Highbridge, unless they removed it. If this is the case, you could also try fighting against a 2 kickbot/1 turret formation.

Your HP is decent for the area, so I expect the turret machina to only do 2000 to one character on their turn. However, that also means that the flamethrower and the turret machina will do 700 to everyone when they use their area attacks. This may mean death if they get three turns in a row. You really shouldn't have full party wipes here. You are not nearly as behind as you think you are.

About Counterattack and Evade & Counter, it works against single target physical attacks AND it checks if they can attack their target validly. Translation: Countering can only be relied on against kickbots.

---------- Strategy 1 ----------- Manmode ----------
Your strategy for grinding should be not worrying about healing your characters with Yuna. Right now, Rikku is your healer. Again, you want your fights to not last long. Switch your Overdrive mode to Stoic or Comrade. Overdrive when possible.

I would suggest using a party that usually has Auron and Rikku in it. Auron actually has HP and he can survive worst-case situations; Rikku can Use Al Bhed Potions to heal or even her Overdrive. STOP TUNNELING ON CURA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAA THIS IS THE VERY DEFINITION OF A MENTAL BLOCK AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Your third can switch among Tidus, Wakka, or Yuna. Tidus/Wakka don't do nearly as much as Auron, but they are faster than Auron, which means that if stuff hits the fan, they can recover the fight with Potions or Phoenix Downs. This approach will carry over to the Seymour fight through a development of your decision making skills.

---------- Strategy 2 ---------- Scrubcore ----------
Your first fight should open with whatever Distill of your choice. Kill that target, then flee, if you really want Yuna to pick up Cura/Protect/Shell. If you're still having trouble after that fight, open every fight with a formation involving Yuna. Switch out the others whenever you want.

Get two turns in on your other members and then summon an Aeon. Have it kill your targets as much as possible. Let it die if it doesn't kill everything on its own and you can not save it using Shield, and then clean up with your remaining characters.

Eventually, you'll get to the point where the Aeons can survive battles on the Highbridge. Charge up their Overdrive meters, and then use all of their Overdrives against Seymour.