In my answer to "Is the Mordenkainen's Sword spell underpowered?", I concluded (and the community agreed) that the spell is terrible. In this question, I will look at what makes the spell unique, how it falls short, and how I can (hopefully) bring it in line with other spells. First, the original:

Mordenkainen's Sword

7th-level evocation

Casting Time: 1 action
Range: 60 feet
Components: V, S, M (a miniature platinum sword with a grip and pommel of copper and zinc, worth 250 gp)
Duration: Concentration, 1 minute

You create a sword-shaped plane of force that hovers within range. It lasts for the duration.

When the sword appears, you make a melee spell attack against a target of your choice within 5 feet of the sword. On a hit, the target takes 3d10 force damage. Until the spell ends, you can use a bonus action on each of your turns to move the sword up to 20 feet to a spot you can see and repeat this attack against the same target or a different one.

Notable problems

• The sword's damage is bad for a concentration spell. Over three rounds (assuming all attacks hit), the sword deals 66 damage, while Bigby's hand deals 108 damage (when upcast to 7th level).
• The sword's damage is bad for a non-concentration spell. Crown of stars from Xanathar's has an hour duration and requires no concentration, but still deals 78 damage over 3 rounds.
• The sword might not even reach its next target. You can only move it 20 feet each round, so an average enemy can kite your 7th-level spell around without much trouble. In my experience, spiritual weapon (which also can move 20 feet) can't reach the next group of enemies at least once per session. Higher-level fights tend to encompass larger areas, so I'd expect the sword to frequently waste a turn moving.

Unique features

• The sword is the highest-level spell that targets a single creature, requires concentration, and purely deals damage. Even if we relax the concentration requirement, only crown of stars (also 7th-level) meets the remaining requirements.
• The sword allows two attacks on the first turn, but only one thereafter. Getting damage out early is usually better than spreading it across multiple turns, but this may complicate attempts to rebalance the sword.
• The sword is one of only four leveled wizard spells that only require a melee spell attack. The others are vampiric touch, Mordenkainen's faithful hound, and steel wind strike.

Goals

1. Keep what makes the spell unique. Making the sword affect an area may improve it, but then it would no longer feel like Mordenkainen's sword.
2. Bring its damage in line with similar spells, without making it overpowered. As the highest-level spell that targets a single creature, requires concentration, and purely deals damage, the sword should be in the running for most damaging single-target spell in the game. The sword should also support upcasting, if necessary, to keep up with spells like Bigby's hand.
3. Improve its speed. It should be able to reach most enemies that aren't actively evading it (and some that are). Moving from one pack of enemies to another should not usually pose a problem; however, highly-mobile enemies, like dragons, should still be able to outrun the sword if they wish to.

Mordenkainen's (sharp and speedy) sword

With those goals in mind, here is my improved version of the spell:

Mordenkainen's Sword (improved)

7th-level evocation

Casting Time: 1 action
Range: 60 feet
Components: V, S, M (a miniature platinum sword with a grip and pommel of copper and zinc, worth 250 gp)
Duration: Concentration, 1 minute

You create a sword-shaped plane of force that hovers within range. It lasts for the duration.

When the sword appears, you make a melee spell attack against a target of your choice within 5 feet of the sword. On a hit, the target takes 7d10 force damage. Until the spell ends, you can use a bonus action on each of your turns to move the sword up to 60 feet to a spot you can see and repeat this attack against the same target or a different one.

At Higher Levels. When you cast this spell using a spell slot of 8th level or higher, the damage increases by 2d10 for each slot level above 7th.

Raising the sword's base damage to 7d10 brings its 3-round all-hits average to 154 (up from 66). This pushes the sword into a comfortable lead over Bigby's hand, which averages 108 when upcast to 7th-level. Given that Bigby's hand can also grapple, push, and provide cover, and can be cast in lower-level slots, losing the damage race makes sense. I considered only raising the sword's base damage to 6d10, but that would mean that an upcast Bigby's hand would still deal more per-turn damage after the first turn.

I added upcasting to prevent Bigby's hand from overtaking Mordenkainen's sword when cast at 8th level or higher. In most cases, higher-level spells deal more damage than upcast spells, so the sword should not be surpassed through upcasting.

Lastly, I increased the sword's speed to 60 feet. My intent was that the sword could reach something and attack on almost every turn. In my experience, it isn't uncommon to have Tier 3+ combats cover more than 30 feet, so I went with the next common range, 60 feet.

Does increasing base damage, improving movement, and supporting upcasting meet my goals for Mordenkainen's sword? Are there any feats or class features that throw its improved damage out of line with other spells? Any play experience with a similarly-modified Mordenkainen's sword would be invaluable. As always, don't forget Good Subjective, Bad Subjective and its call to Back It Up!