Best caliber for AR pistol

Hi all, have a question about the AR pistols regarding barrel length, reliability and ammo.
I would like to build a pistol with a 7.5 inch barrel but if I'm reading correctly the barrel being that short causes a lot of problems.
I'm reading that the following things are problematic:
1- accuracy suffers because the barrel is too short to stabilize the bullet
2- at 7.5 inches the powder charge doesn't have the time to burn and you blown half of it out into a fireball
3- the short barrel will not reliably cycle the BCG and it will cause reliability issues

All those are big issues, but are there ways to overcome some of those?
Also, I was told that a .300 blackout or .300 AAC are better choices for a pistol, is that true?
I was told I would be better off with a pistol caliber AR pistol, but I want to keep the power of a rifle cartridge.

Lastly, I know a pistol with a 7.5" barrel isn't the most accurate, and I'm not looking for a sniper rifle. I want it to do the job between 100-200 yards.

Is that doable?

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Best caliber for AR pistol