How can I hang a ceiling fan with a 3/4 inch difference between the junction box and bracket?
There is a 3/4" extender sold by Cooper Industries (and maybe others). They call it a cover. This site sells it and it probably can be found elsewhere online.

You need to be sure that the box in the ceiling is firmly attached to the framing, preferably directly screwed into a joist. Fan rated boxes have heavier duty attachments for the fan hanger and use longer screws.

Then you need to make sure that the fan hanger is firmly attached.  I would attach it directly to the ceiling box, not just the extender/cover.