Perfect spirit?

[ordinaire]

Hello!

I was wondering if anyone could help me with answering a few questions:)
I've read around but I couldn't find a topic for this.

I wish to make a really, really neutral spirit, similar to top shelf vodka or better.
Is this possible using home equipment? And what would I need in order to succeed?

At the moment I only have a copper alembic/pot still for 5 liters. This works perfect for what I use it for; distilling herbal spirit(gin/anis/absinthe) using a neutral spirit as base.
I usually use vodka or eau de vie for this. -That works great, but this is getting expensive where I live.
Recently I tried switching the base spirit with local moonshine(circa 90percent pure alc), but the "moonshiny" taste ruined the result.

So my question:
Is it possible to clean up the moonshine I get here using the pot still, if I distill it several times? Or do I need a reflux column or something for this?
I need it to reach minimum vodka-level quality (stolichnaya or preferably better)

As I understand a pot still is good for making whisky & gin etc, as it does not make too pure a distillate.
So I'm thinking I might not be able to make a good spirit out of this moonshine with this still. Or can I achieve this if I run it 4-5 times?
I'm not afraid of the extra work, but if it's futile I'm grateful for anyone who can tell me before I spend a whole weekend running the still:)