Song titles are highly variable. Ones marked with an asterisk could use a remix.
Overture [DQI]
Well, duh. Maybe the single most used song in video games. Most games have a slightly different variation on this one; I like DQXI's the best, but I could see them using DQIII's because... y'know, Erdrick. That version of the overture is actually titled "Roto" in DQIII's soundtrack as opposed to the usual "Overture (number)", so I guess you could consider it Erdrick's personal theme in addition to being the main theme of the series.
Unknown World* [DQI]
The first game's overworld theme, it also shows up in DQII and DQIII when you visit Alefgard, at least from the SFC versions onward. If Erdrick's stage is set anywhere in Alefgard this is a must-have, but it's not exactly a fast-paced battle tune, so a remix is probably necessary.
Traveling With Friends [DQII]
AKA "Traveling With Two Coffins", DQII's overworld theme once you've got the whole party together. It also plays when you complete a mission in the Heroes games, and honestly that's what I associate it with most. It captures the fun and upbeat spirit of Dragon Quest really well.
Fighting Spirit* [DQIII]
DQIII's battle theme. It's pretty good on its own, but since it's Erdrick's own fightin' music a remix would be appropriate.
Adventure [DQIII]
Yet another overworld theme, this one's a rousing march. Definitely my favourite overworld theme of that type. It's also used at a certain point in DQXI, so it's relevant, for whatever that's worth.
Hero's Challenge [DQIII]
DQIII's final boss theme, one of the best ones in the series. It's great, it plays when Erdrick takes on his ultimate foe, and it's got some of the overture in there. Some other game might also use this song prominently, like for the ultimate final boss or something, but that's a big secret.
Battle for the Glory [DQIV]
DQIV isn't connected to DQIII or Erdrick at all, but I can't imagine it not sticking its toe in somehow. It gets overlooked a lot over here, but it's hard to overstate what a big deal DQIV is in Japan. This is DQIV's normal battle theme, which has also appears in DQX and DQXI. DQXI plays it when you fight in an arena, as a reference to Alena's chapter in DQIV. That definitely works for Smash.
Great Battle in the Vast Sky [DQVIII]
An intense variation on Heavenly Flight, the song that plays when you ride Ramia in DQIII. DQVIII uses it as its final boss theme, where... hey, guess who gives you a ride? Heavenly Flight is too sedate for Smash, but this version would fit in fine while also repping DQVIII. Two godbirds with one soulstone,
ahem.
Unflinchable Courage [DQXI]
The battle theme from the most recent/upcoming game in the series. Hear it in Smash, then fire up DQXI S and hear it in its natural habitat within five minutes. Easy.
Light Through the Leaves of Love* [DQXI]
Yggdrasil's theme and the all-purpose love theme from DQXI, it plays during a lot of the game's more emotional scenes. OK, this one might be a stretch, but I think it could be arranged into something really epic, maybe with some haunting vocals goin' on. It does technically have lyrics, since it's an in-universe song written by the ancient sage Serenica. It's only six lines and I don't think they actually fit the music at all, but it's a start.
Battle of the Monsters [DQM]
The battle theme from every game in the Monsters subseries, which is pretty ridiculous, but it's a good, goofy song. It'll absolutely be in the next Monsters game, which we might even get this time.
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Runners-up from the Even More Never Gonna Happen pile include anything from Rocket Slime, Blessing of Anlucia from DQX, a DQVI Medley, an Intermezzo Medley, Go For Broke from Swords, and a deliberately annoying vocal version of Stella's Theme from DQIX. I especially want that last one.
