I can cornfirm this behaviour on my tachyon as well..
I cant give you an advise here but another observation: The few times it happened to me it was, as you call it, a depletion.. and since the Tachyon needs its battery to start booting anyway i guess that there is not enough voltage coming from the battery to enable the poweron. I dont want to sound too pessimistic but i think that, since it is an hardware issue that the battery is mandatory (so thanks for the gift due to tarriffs, right?) that it feels unlikely that there is a simple software switch for this. If i had to mitigate this problem i would rather consider trying to shut down the tachyon safe before depletion to prevent this from happening.
i havent checked it yet… but does this also happen if you power through the hat power pins?
If i get this ( Will the battery always be necessary? - #2 by rickkas7 ) correctly, then the battery is not mandatory when powered through the connector directly.. so maybe you could have a boot on power on that way?