At the risk of starting a flame war on things that are borderline for discussion. I know for a fact that twice distiling mollasses wash and then pulling it off at aezetrope (95.6%) will
not remove the mollasses flavour, merely refine it.
Think white rum such as Bacardi.
Full flavoured rums are often produced by blending mollasses or caramel, mostly the cheap and nasties from distilleries in countries where fine rum is not a tradition. A lot of the finer rums from around the world are matured in oak vats and barrels and get their colour and some of their flavour that way.
As in beer, different distilleries use differnt methods to produce different types and flavours of rum. And like breweries, each distillery has it's own take on things.
Rum is not as strictly controlled as Bourbon (which is produced in only one county and has very strict controls on everything from ingredients to abv and storage) as it's a global product with many different bases and variations. Things like cachaca and other cane based drinkls also fall into this class.
You won't get rum from adding neutral spirit to a barrel, but you may be able to give it a rum like flavour by adding some mollasses and then filtering or adding some commercial cordial.
As far as the difference tween cordial and a proper ferment, how would you look at someone who did a sugar wash with turbo yeast and then tipped a satchet of beer flavouring into it then told you it was the same as allgrain? Even if they said they'd filtered it
I've seen the prison hooch responses here to questions like this so no need to answer. :lol: