I think you are doing it backwards. You begin with the spell and try to make it fit what you think you want, but that requires you to do a good bit of extrapolating and predicting the outcome. But most of the listed spells are situational, so you can't know when a tweak intended to increase utility will become, in one particular situation, overpowered.

My recommendation is to discuss with your spellcaster players their reasons for selecting or rejecting specific spells and then attempt to tweak from there.

Animated Rope, for example, is a highly valuable spell when mounted foes must charge through a limited space to attack the PCs. With one second level spell you can stop a cavalry charge, potentially dealing more HP in falling damage than a Level 3 Fireball. Does this kind of situation arise often enough to make the spell valueable? Your players will know.

There is no such thing as balance. Like the Questing Beast, it has eluded the very best DMs grasp since Expert Edition was published. I can show you spoor if you like. However, your campaign will assume certain norms, and spells virtually useless in your campaign might prove overpowered in mine. The trick is to make the less appealing spells more appealing, whether by increasing the raw power of the spell, or by creating scenarios where such spells are more valuable.

Animated Rope might be an invaluable spell for a party climbing a mountain or delving into a cave. Especially if minmaxers didn't bother with Climb skill during character creation. So, the prize the party seeks is in a monastery atop a mesa. That second level spell slot now assumes much greater utility.

The purpose of magic is not to inflict damage like a fighter; that's why you have fighters. Video games have impacted this philosophy by 'balancing' the classes based on damage output. But D&D is not a video game. It is a form of collective storytelling in which drama and narrative become more important than the mechanics of the fight. A video game supplies the story and only leaves the fights to the player. A D&D game session can be played without a single fight happening and the players provide the story.

So, resist the first impulse to balance things and instead run your game. You can always adjust later to decrease the desireability of overused spells and increase the desireability of underused ones. Sometimes simply by taking your players in directions they never imagined.