"By transitive property, the only transactions that should count are ones that convert USD to anything, and ones that convert anything to USD."
According to US tax law, any accession to wealth is taxable when the gain is realized (yes, there are exceptions to timing and basis). So, if you mined a BTC and spent $1 doing it, then used that 1 BTC to purchase some LTC when the value of the BTC was $100, you gained $99 at the time you traded it for LTC. That gain is realized at the time of the exchange and taxable at that time.
According to US tax law, any accession to wealth is taxable when the gain is realized (yes, there are exceptions to timing and basis). So, if you mined a BTC and spent $1 doing it, then used that 1 BTC to purchase some LTC when the value of the BTC was $100, you gained $99 at the time you traded it for LTC. That gain is realized at the time of the exchange and taxable at that time.