dhenry:
I don't seem to be able to find the ATTiny's current consumption anywhere
The datasheet is the best source for that.
A rough estimate would be 20ma, worst case scenario. Typically a few ma.
I just had a look at the datasheet myself, it's quite detailed.
Worst case is actually about 14mA (running at 20MHz with everything turned on).
At 8MHz ... about 6mA, easily within a 10mA target.
At 1MHz with timer1 + ADC powered down... more like 1mA.
PS: Turn off timer1 first! Timer1 actually uses about three times as much power as the ADC (and ten times as much as timer0 - weird!).