Strangely enough, I'd been thinking of writing an omake of my own about Homura's trial-and-error approach to interpersonal relationships. I wasn't really satisfied with it, but this convinced me to go back and revise it a little. Here goes nothing!
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How to Make Friends with Mami Without Really Trying
The rusted remains of a thousand thousand cars littered the insides of the barrier, forming a vague line that stretched into the illusory horizon. From the view of this spire, high above the ground, Homura noted with a vague sense of amusement that they resembled nothing more than a company of marching ants, stark and dull against the vibrant blues and greens of the glassy floor.
Beside her stood an unlikely ally, and the present source of her uncharacteristic invigoration: Mami Tomoe. For the past few loops they'd gotten off on the wrong foot, though Homura insisted she was at fault for precisely none of these. How was she to know Mami wouldn't enjoy her own life-sized Kyouko-pillow, or that Kyouko would react so violently when she found her own Mami-pillow? After these last few failures, Homura had shelved that plan for future testing on Sayaka. Now she had a new plan, an idea carefully crafted to immediately and permanently put her in Mami's good graces, no matter the condition of the loop.
"Well, Akemi-san, are you ready to begin?"
Homura looked up, jostled from her musings. "When you are."
In a flash, Mami sprinted down the side of the spire, Homura only a fraction of a second behind her. Ahead of them loomed the twisted forms of this witch's familiars, tall, bright, and elongated human shapes that looked remarkably like taffy.
A confident smile bloomed on Mami's lips.
"Regale!"
Immediately, the familiars found themselves bound together by golden ribbons, and just as quickly blown apart by Homura's follow-up assault.
Spinning around, Homura let loose a barrage of bullets, back to back with Mami doing the same: "Tiro Volley!"
Familiar after familiar fell to the combined assault of the two magical girls, relentless in its ferocity. Wave after wave advanced, shambling like zombies, until at last none were left--all was silent, save for the light panting of two girls trying to catch their breath.
The question was coming now. Homura had carefully chosen this time, this place--her friendship with Mami came now.
"Akemi-san," Mami began with an exhausted smile, "you always take things so seriously. Why don't you do what I do, and have a little pride in your attacks?"
"Pride?"
"Your attack names!" Mami shouted, hands on her hips and a finger raised in mock accusation. "Or should I say, your complete lack of them. You're a magical girl, Akemi--no, Homura-san. So start acting like it!"
Before Homura could respond, the ground began to pulse, and a growing trail of sparks began to coalesce from the bodies of the fallen familiars, growing into an amorphous cloud of shining, metallic fog.
"Chance!" Mami grinned. "Now, fall back and I'll show you how it's--ah?"
Homura had vanished. Glancing about, Mami began to back away when she noticed the cloud seemed distracted by something. Fixing her gaze in the same direction, she could only stare in confusion as Homura struck a pose atop an old Volkswagen Beetle, arms folded across her chest.
"Very well, Mami-san, I will show you my pride!"
Homura leveled a stare at the approaching witch, then shouted in English:
"<Automotive Explosion>!"
"Homura-san!"
Fire burst from a truck ahead of her, consuming the witch in a fireball large enough to entirely obscure it from Mami's vision for a moment.
But the other magical girl wasn't done. In a moment--how did she even travel so fast?--Homura was down among the wreckage, launching the truck's engine at the oncoming witch.
"<Blooming Vehicular Soul>!"
"Homura!"
Again, the golden figure was obscured in a dazzling explosion, followed by a shockwave that sent Mami stumbling back in a daze. That exquisite phrase, that exotic allure of the English tongue--again!
Mami nearly missed it, as Homura appeared again near the Beetle she'd been standing on only seconds before. Lifting the vehicle with an effort she clearly wasn't accustomed to, Homura grit her teeth and held it ready in the air.
Mami was struck with the image out of many a jidai-geki film, a samurai standing--tense--ready at any second to take his opponent's life.
Then, with a scream, Homura dashed at her opponent:
"<Seven Phoenix Shining Fahrvergnügen Blade of the Department of Motor Vehicles>!"
"<Darliiiiing>!"
Homura froze. Before she'd even had a chance to land that final attack, Mami appeared before her, her signature cannon in hand.
A line of saliva ran from the corner of her mouth, and a glazed look covered her eyes.
Turning, Mami let out a primal roar:
"Tiro Finale! Tiro Finale! TIRO FINALE!"
Three sharp blasts, each louder than the last, shot three fatal holes into the now-vanishing witch. In a single continuous movement, Mami tossed aside her cannon, swept Homura into her arms, and bent down in a romantic embrace.
"Kiss me, <Darling>."
As she stared at the incoming kiss, approaching at what seemed a glacial pace, only one thought crossed Homura's mind:
Why haven't I tried this with Madoka before?