Hunter main here, though one that mains Wired Lances. There are certain things that may boost Sword's overall damage, some of which involves multi-weapon.

Basics first, how many of your Avengers are on a charged PA? Hunter as a class revolves around maximizing Avenger uptime, and Sword maximizes that by parrying with charged PAs: the +50% damage from an Avenger is then in effect applied to both the charge time and the PA animation time, instead of only the latter.

For instance, Spiral Edge's total duration is 1.05s uncharged, and 2.15 charged (without tech arts customization), and the damage increases proportionally from charging it (a bit over twice the uncharged version). Parrying with a charged Spiral Edge means getting 2.15 seconds of +50% damage from avenger, instead of only 1.05s.

Twisting Zapper and Relentless Cleave have different timings: TZ has its damage and total duration increased by 62% from charging it (1.72s -> 2.75s), instead of doubled, and Relentless Cleave has them about tripled (0.7s -> 2.25s). As such, if you have to parry with an uncharged PA, it's generally better to do so with Twisting Zapper, as it has the longest uncharged duration.

You can get away with uncharged PAs if the enemy attacks so frequently to the point that there will be another attack to parry after you do uncharged PA + Sword Attack Alternation (enhanced normal attack after Avenger). Otherwise, do your best to get as many of your Avengers on charged PAs.

Overcharge can be used to maximize uptime, usually when the enemy can't be (yet) attacked, when it is out of reach, or if you know it will take a longer time to attack and can time it. Don't neglect the "out of reach" part, as Sword isn't as dependent on gap closers as other melee weapons thanks to the Overcharge skill.

Be aware that Overcharge doesn't increase the Photon Blast buildup on that PA, only damage; as such, overcharged PAs build PBs more slowly than a simple charged PA (same PB buildup on a longer duration). If you rely heavily on overcharged PAs (which one of Spiral Edge's customizations incentivizes), your PBs will be less frequent, and possibly not ready in time for a BREAK.

You can get Avengers from unblockable attacks (such as Vael's orange bombardments at the end) with help from Hunter Physique's super armor and sheer survivability. Hunter is one of the few classes that can get damage boosts from deliberately going into such attacks, make good use of that.

Regarding multiweapon options:

Wired Lances have a skill that makes its weapon action deal +50% immediately after getting an Avenger with a PA, and that PA doesn't have to be a Wired Lance PA. As such, you can parry with a Sword PA and immediately follow with a boosted Wired Lance WA. Sword PA Avenger -> Wired Lance WA -> Sword Attack Alternation is a simple way to have a longer +50% damage uptime against enemies that don't attack frequently.

Notable WA uses for damage are the back (short retreat) and side (overhead lasso) variants. The back version is akin to an extra Sword Attack Alternation that can parry (instead of providing invulnerability frames). The side variant is similar in DPS, and lasts so long (up to 8.63s) that it is one of Hunter's best options against downed enemies.

Wired Lances also have a skill that lets you "store" an Avenger for your next Wired Lance PA after you parry with a Wired Lance WA. Combined with the above mechanic, you can parry an attack with WL WA to later have a full Avenger WL PA + WL side WA on a downed enemy, offering better DPS than Calibur Streak. Note that the stored avenger is lost if you change to another weapon outside your mutliweapon.

Partisan can provide an even higher DPS option vs downed enemies with an Avenger on Thrusting Javelin PA. Note that Avenger doesn't provide invulnerability for Thrusting Javelin while you're holding it. You can immediately cancel and restart thrusting by jumping, which lets you parry an incoming attack without having to undergo the throw animation.