If you had the means to do it you could maybe take this method to the next level, I think. If you had a big plastic tub that you could fill with water and fit in your freezer, and something like a plastic tray to stand it on to keep the condensation off your floor, that would further cool the air from the fan, wouldn’t it?
It would be down to the logistics of having the space to freeze the tub in the first place, but a 2lt ice cream tub might do the trick? Once one was frozen and in use, another could be in its place in the freezer getting ready to replace it.
Disclaimer: Would be a massive hardship to have to consume the ice cream first, so I am fully aware of the totally negative aspect of this suggestion.