I heard that one can use thionyl chloride to dehydrate it, but I'm not really sure if it would be available for amateur chemists since it's listed on the UN Convention for (the Elimination of) Chemical Weapons.
And no, I'm NOT thinking of getting cryolite either.
I think obtaining anhydrous aluminium(III) chloride from hexahydrate $\ce{AlCl6 · 6 H2O}$ isn't worth it, both economically and time-wise. Thionyl chloride might work, but, as you said, it's an unpleasant reactant to work with, which is also likely more expensive than dry $\ce{AlCl3}$ (or is on par, depending on the purity of aluminium trichloride).
A common way to prepare water-free $\ce{AlCl3}$ in the lab is to heat pure aluminium metal with the excess of dry $\ce{HCl}$ gas at $\pu{150 °C}.$ The product is then sublimated (above $\pu{180 °C}$) and collected in the condenser (air-cooled). The quirk here is you have to make sure pure aluminium is used, not an alloy; but this is usually evident from the color of the product, which should be white/colorless.
If you already have $\ce{AlCl3}$ labelled as anhydrous, but you suspect it was slightly moisturized, it can be regenerated via sublimation [1, p. 636]:
Aluminium chloride (anhydrous) […] Sublime it several times in an all-glass system under nitrogen at 30-50 mm pressure. It has also been sublimed in a stream of dry $\ce{HCl}$ and has been subjected to a preliminary sublimation through a section of granular aluminium metal.
An extensive description is provided in Experimental part in [2, p. 1230]):
Aluminum Chloride.—The aluminum chloride (Baker Chemical Company) was purified by subliming three times down a straight Pyrex tube (with constrictions) which contained a small amount of nitrogen gas (50 mm.). In the first sublimation, the aluminum chloride mas sublimed through a section of granular aluminum metal, which was supported with plugs of glass wool. After the final sublimation and before sealing the tube off, aluminum chloride mas sublimed back down the tube until the remaining material formed a loose plug.
In order to remove the aluminum chloride from the tube, the tube is scratched and then the scratch touched with a hot rod in such a manner that the tube cracks but does not open. The tube may then be weighed, the tube tapped slightly to open. and after removing the aluminum chloride, the empty tube weighed. Using these techniques, it is possible to prepare very pure samples of aluminum chloride and weigh and transfer them without bringing them into contact with air.
Remember to store anhydrous $\ce{AlCl3}$ in an air-tight vessel and perform all operations with it in a fume hood. Also, keep in mind that you can purchase $\ce{AlCl3}$ dissolved in organic solvents such as nitrobenzene, THF, or even $\ce{AlCl3}$-functionalized silica gel.
I recall a paper where heating the hydrate in a stream of $\ce{HCl}$ gas avoided the formation of a basic salt.
This may work for hexahydrate $\ce{AlCl6⋅6H2O}$ also.
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