The above procedure has been tried twice on benzodioxole with 1.05 and 2 equivalents of propionic anhydride, both times with 2 equivalents lithium perchlorate and with stirring for 2 hours at 60oC. Both times, nothing was recovered but benzodioxole :( ; at least it wasn't demethylated at that temperature as would have happened with any other Lewis acid. The procedure will be attempted again soon with anisole (possibly at a higher temperature) and if that doesn't work, a mixed trifluoroacetic acid-propionic acid anhydride may have to be employed. The mixed anhydride would lend itself to a couple of interesting possiblities :)
A 32 page document singing the praises of lithium perchlorate can be found at http://www.gfschemicals.com/technicallibrary/anhydrous_liclo.pdf (http://www.gfschemicals.com/technicallibrary/anhydrous_liclo.pdf)
There are some interesting methods which could be useful for our purposes:
The first obvious one is on page 18, with the rearrangement of allyl vinyl ethers to aldehydes. If this could work on an aromatic system it would be very good news. Page 19 has the conversion of epoxides to carbonyls in good to excellent yield.
Page 21 has some rather interesting epoxide and ring opening reactions, which could be a very interesting pathway to the BOX series, and page 22 might be interesting if that alpha,beta-unsaturated carbonyl could be replaced by nitroethane.. There's more, and it's worth a look.
An important note on safety. Lithium perchlorate seems the safest to work with of all the perchlorate salts, but it still isn't something to mess around with. There is a useful link for anyone who ever finds themselves confronted by perchloric acid or any of its salts, and wants to know how to safely make good use of them: http://www.gfschemicals.com/technicallibrary/perchloricacid.pdf (http://www.gfschemicals.com/technicallibrary/perchloricacid.pdf)
It may be interesting to consider lithium iodide, or even bromide as suitable alternatives to lithium perchlorate. All are lithium salts of strong acids with approximately equivalent pKa values of around -10, and both lithium iodide and perchlorate are soluble in organic solvents; lithium bromide is soluble in alcohol but I'm not sure about ether.