I do have a conical fermenter and use it sometimes. I will ferment in it and rack it after fermentation is done. Usually about 20 days. I’ll let it set for a month to clear up and rack again then bottle it. But even still with some wines it still comes out with the off flavor.
20 days is to much in the primary
to much head space
When I start a Wine if in a bucket I keep it in for a week or even 5 days (prefer about 5)
I stir to give it Oxygen, and cover with a towel (Yeast stage aerobic (needs air)
The secondary I make sure to have the racking cane up against the wall of the carboy
I sure fill this to the top (Yeast stage anaerobic ferments without much air )
I also Want to have tannin this can be black tea , and acid
doesn't sound like your problem,
but low acid can be bad
With A wide Mouth int he primary for so long it should oxidize
even though C02 is heavier then air , and floats above
Air will get in (I suppose the tubulance of the c02 coming out from must)
or cap of fruit when you stir or push down)
If you want to do a experiement even without sulfites
just ferment juice in a carboy from the very begining
I do not like the idea (your not getting as much oxygen in the primary,)
but could see if your wine still suffers cutting out the open mouth container,
all in all 20 days in the conical fermenter (even covered sealed with airlock)
is to much head space
sit a beer out in a can at a party oxidizes more , the next day
filled in a bottle to the spout or neck less with less air space.