The dehumidifier should be running continuously, not shut off for days at a time. Use a hygrometer and keep the basement humidity well below 50%.

The mould is not just in the basement but in your HVAC system, so shutting off the basement may not do all that much to reduce the odour.

Ok. Thanks. We actually gutted the basement down to the bare concrete walls and floors, used and anitmicrobial cleaner to kill any mold and KILZed it. We were surprised that the smell got worse after we did so.

Attempting to kill all mould instead of cleaning and removing mouldy materials is a futile task, according to Inspectapedia. ( See link.) Kilz is for stains.

And there is no alternative to mechanical dehumidification to keep basement RH below 50%. AC is partially effective. But as homes have become tighter, it doesn't run long enough to do the job. Mould is always in the air. But humidity plus food enables it to grow to annoying quantities.

Here is a link that might be useful: Cleaning Mould

In my basement I have two dehumidifiers located in different places with humidistats controlling the receptacle for the dehumidifier. The units themselves are set at the minimum humidity and the humidistats at slightly blow 50%. One of the units drains directly into the floor drain and the other will do so eventually.

If you have leaky return air duct work the basement,its sucking basement air into your home upstairs. What do the walls look like? can you seal/close the windows? Any bulk, liquid water, draining from your a/c or dehumidifer, needs to be draining into a covered drain. Insure your basement is seal as much as possible. Stop the mirgration of vapor into your basement 1st. And your stop the mold growth. If your have ground..it must be covered. if you have concrete, with lots of cracks, seal them...U may consider sealing the concrete floor...but this isnt the place for anymore of this information. Get a pro involved.