This is probably more straightforward advice than you're looking for, but my primary strategy is to give the DM everything he needs in one post, or at least as much as I can with the information I have.
At the most basic level this means providing both attack and damage dice, whether or not I know that the attack will hit, but this also extends into other actions. At the table, you can have a quick back and forth with the DM while you decide on your actions. In a PbP, such a thing can take days.
So, instead of narrowing the options and then declaring what you're going to do, cover a wider range of actions. Example:
I'll attempt to stealth out from behind the rock (Stealth roll: 1d20+5=13).
IF I haven't been detected by the orc holding the hostage, I'll try to kill him from behind with a Sneak Attack (Attack: 1d20+6=14; Damage: 1d6+1d6+1d4=12)
IF the I am detected by the orc holding the hostage, I'll immediately shout for him to surrender (Intimidation roll: 1d20+2=7).