Endless_snow
Ok so first of all I want you to keep in mind that MC is not Levi Ackerman, he have his body but he doesn't have his personality nor memory. I once saw another fanfiction about someone reincarnated with Accelerator's power in My Hero Academia, turns out he did the same as you, trying to make it Accelerator in MHA not with his powers but being him. Ultimately that author self-destructed due to him not knowing enough about Accelerator's personality. Secondly don't limit your MC to the original Levi, he isn't him so he can use different fighting styles and weapons, different hobbies as well... Also longsword are known to be extremely huge and heavy, but actually the blade is slightly longer than a meter and weight about 2 kg. So even Levi can use one without problem.