What to do with low quality strip/low wines

[lex]

G'day from Australia!

A few weeks ago, I inherited my grandad's fermenting/distilling stuff.
I've successfully made half a batch of wonderful spirits following many guides on here, particularly the one by Mozr. Cheers mate! (I say half a batch, because I'm currently collecting tails on my first spirit run, and even before filtering it smells better than store-bought vodka).

Some context: my pop made really low-quality stuff. He only used granulated sugar, no carbon, no clearing/finings, and he only distilled once with dirty, lees-filled wash. So basically, I've got about 50L of his spirits, which are essentially a low-quality stripping run. And he drank it every day!

My question is this: if I re-distill his low wines, collect fores, heads, hearts, tails, filter it -- the lot; will I still get a product that approches the quality of what I have made so far?
Or is it better just to dump the lot?

Thanks to every poster for all the invaluable help so far. Every question answered on here has helped me to make a great product.

-Lex

[Mash]

Run it. The quality is in there, you need to refine it.

[H12rpo]

Yep run it.....you’ll get quite a haul off a 50 litre strip batch

[gaza the instructor]

Yes buddie run it and stick to plan "A".

[Easydrinker]

I have been beaten to the answer, but dilute your pop's stuff to sub 30% and take the good stuff out of it with another run through the still.
Waste nothing but waste.
Meaning no disrespect to your pop's here,but YOU may live a little longer if you drink cleaner spirit.

Robert.

[lex]

Thanks for the answers, guys.

I'll see how it smells and tastes after I run it in a weeks or so, and I'll come back with the results, if anyone is curious.

Would be interesting to see if you can still get a decent product by distilling well, while cutting corners with the wash.

Cheers

Meaning no disrespect to your pop's here,but YOU may live a little longer if you drink cleaner spirit.

Haha fair enough. I'm not a big drinker of spirits anyway, but I like the hobby. I'm just glad I can still put pop's stuff to good use.