3 miles per hour

Actions in Combat are not relevant to the travel pace rules. Rogues are faster movers in combat thanks to Cunning Action, but so are most characters as a character's walking speed reflects:

Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round. This number assumes short bursts of energetic movement in the midst of a life- threatening situation. (PHB 181)

[courtesy of MisterB in the comments]

Cunning Action and the Dash action do not affect travel pace. Compare this to a feature like the Totem Warrior Barbarian's Elk Aspect of the Beast which directly mentions travel pace:

Whether mounted or on foot, your travel pace is doubled, as is the travel pace of up to ten companions while they’re within 60 feet of you and you’re not incapacitated (see “Adventuring,” for rules on travel pace). The elk spirit helps you roam far and fast.

What about Longtrider?

Longstrider would increase your travel pace most likely. Travel pace of 3 miles per hour is derived from the common walking speed of 30 feet. According to the Dungeon Master's Guide:

In 1 hour, you can move a number of miles equal to your speed divided by 10.

Since longstrider increases your speed, your travel pace also improves during the duration (which by default is 1 hour).

Why can't I just Dash?

Combats rarely last more than a couple minutes and require a character to do a lot of things that would be very physically taxing should they be done for extended periods of time. In the rules for Chases from the Dungeon Master's Guide this is made apparent by this section on dashing (mentioned in HellSaint's answer):

During the chase, a participant can freely use the Dash action a number of times equal to 3 + its Constitution modifier. Each additional Dash action it takes during the chase requires the creature to succeed on a DC 10 Constitution check at the end of its turn or gain one level of exhaustion.

While this isn't directly related to travel pace it demonstrates that staying in combat mode for long periods of time (in order to Dash) could quickly result in exhaustion before you simply can't move further.

Major image only lets you create one image of yourself

an object, a creature, or some other visible phenomenon

Note the singular there. Only one illusion of one creature can be created by the spell.

Does the purview of "some other visible phenomenon" cover me here? I'm not trying to "break" the spell necessarily; what I'm trying to create is a visible phenomenon.

No, it doesn't. Note that it says "other" visible phenomenon. That means visible phenomenon other than the two categories (object and creature) previously talked about. It doesn't mean "other phenomena" in the sense that you can ignore the limitations previously mentioned in the spell. The phrase is only there to allow you to create non-creature, non-object illusions (eg a rainbow or fog).

If major image was designed to allow this they would not have put the words "a creature" in the first line of the spell. Instead they would have said "objects or creatures or other phenomena". But they didn't and thus the RAW of this spell simply does not allow it to be used in the way that you want it to.

There is already a spell that does exactly what you want to do: mirror image

Mirror image says:

Three illusory duplicates of yourself appear in your space. Until the spell ends, the duplicates move with you and mimic your actions, shifting position so it's impossible to track which image is real.

This is exactly what you are trying to do with major image and since it won't work with major image you should just use it instead. The spell is literally tailor-made to achieve the effect you wanted. Mirror image is even a lower spell level than major image so you can get the same effect by using less resources.

Major image and mirror image are different spells that are designed to do very different things

Mirror image is a one trick pony; all it can do is create illusory duplicates of yourself to aid you in battle. Useful if you want that one particular thing, but not so useful otherwise. Major image is a very versatile spell that can be used for all manner of strategies both in battle and out. It can create illusory hiding places. It can create illusions of threats to scare off enemies. You can create illusion of treasure to set up a trap. You can create a single illusion of yourself to talk to the enemy leader and avoid exposing yourself to danger.

They are simply two spells with two different effects and ways they were designed to be used.

Regardless, the wording of major image explicitly shuts down what you are trying to use it for, it simply was not designed to duplicate the effects of mirror image.

^{Even if major image could duplicate mirror image's effects (again, it absolutely cannot), it would be strictly worse than mirror image in just about every way in doing the one thing mirror image was designed to do.}

^{1. Major image uses a higher spell slot}

^{2. Major image requires concentration (mirror image does not)}

^{3. Major image requires you to use your action to make the images move with you (mirror image does it for free)}

^{4. Major image disappears upon simple physical examination or an ability check. Mirror image requires each image to be hit with an attack.}

^{5. Major image’s illusions disappear at the same time. Mirror image only has the hit one disappear.}

^{There is simply no conceivable way that using major image the way you imagine it would be better than using mirror image instead.}