I was pretty convinced that Alphinaud's BSB would be the key to sub-30ing this, but after falling just a little short, decided to try a full fire team, which got a little extra boost from using Belias as my main magicite instead of Syldra. Had a couple very close calls, then got a little more aggressive with my magicite deck by using a double Spell Ward Madeen instead of a a double Spell Ward Famfrit, and the result was a 29.54s victory, with just one 6* SB!
LD Yda / BSB / R3 Ironfist Fire + R3 Meteor Crush / +30% dmg RM / double fie boost / major fire resist
LD Alphinaud / SSB / R5 Lunar Ifrit + R3 Hastega / Mako Might / zero fire boost / synergy earth + fire resist
LD Papalymo / USB / R5 Chain Firaja / Gathering Storm / double fire boost / synergy earth + fire resist
PD Y'shtola / BSB / R3 Shellga / DMT / major earth resist
LD Cid Garlond / no relics used / R3 Burnt Offering + R5 Entrust / +30% dmg RM / single fire boost / moderate earth + fire resist
Bonds of Historia as RW
Belias (+L15 Empower Fire, +L15 ATK Boon) as main magicite; King Bomb (+L15 Empower Fire) and Madeen x3 (+L8 Spell Ward x2, +L20 ATK & MAG Boon, +L8 HP Boon, +L10 Fast Act) as subs
I had been trying more complicated Entrust scenarios, but ended up finding I could get by with just one early Entrust from Cid to Y'shtola. This was because if going fast enough, Y'sh only needed one BSB cast after her opening use of it. She needs to use it so the Stoneskin absorbs a decent amount of the first Incubus Tank Purge, even if the P2T2 Radiant Plume hits after the bubble goes up.
Either way, there needs to be enough HP so that with what's remaining after the first Tank Purge, plus a 2.2K Cmd2 medica, everyone can survive the next Incubus Tank Purge, too. This means that a Deathgaze would be better than a third Madeen, since everyone's low on health for Phase 5, but I haven't made an inherited Deathgaze yet. I imagine the Full Breakdown from Yda's BSB helps to survive all this.
One other thing that might be key is that I was able to get Pap's last Chain Firaja off before Gathering Storm ran out, which normally I hadn't quite been able to do. So he got an extra full-power chase out of that, because otherwise it wouldn't land within the 15s USB window. (Normally instead of casting the Chain Firaja, I'd go GSB -> USB - Chain Firaja, so this was clearly better.) Temporarily turning the new Auto mode on (with Abilities on and Soul Breaks off) can probably help reduce input lag in situations like that.
Approximate turn order:
Yda: Ironfist Fire x2 -> Meteor Crush -> BSB -> Ironfist Fire x4
Alph: Hastega -> SSB -> Lunar Ifrit x6
Pap: Chain Firaja x3 -> USB -> Chain Firaja x6 -> USB
Y'sh: BSB -> Shellga -> Cmd1 to Alph -> Cmd1 to Yda -> Cmd1 to Cid -> BSB -> Cmd 2 -> Cmd1 to self -> Cmd2 to Cid -> dies
Cid: Realm Chain -> Burnt Offering -> Entrust Y'sh -> Belias -> Realm Chain -> Burnt Offering x2
Here were everyone's important stats:
Yda: 8890 HP / 309 DEF / 290 RES / 658 ATK
Alph: 8227 HP / 336 DEF / 486 RES / 819 MAG
Pap: 8261 HP / 258 DEF / 416 RES / 678 MAG
Y'sh: 6791 HP / 382 DEF / 514 RES / 674 MND
Cid: 9170 HP / 399 DEF / 300 RES / 559 ATK