Put a NLT date on the cover page and tell them you're hand walking it because it's time sensitive, but only if they ask.

Otherwise, have your LPO/CPO/DIVO sign off on that shit on the spot.

For DH/CMC, hand it to them and ask if he can sign it right then. If he says no, then just place it in his inbox and tell him the NLT date. Come back to check his outbox once in the morning and once before COB every day until you get it back.

For XO, just put it in his box and let him know it's there and the NLT date. Continuously check his outbox at his office/admin, but give him a reminder once every three days or so.

For CO, same deal with XO.

Also, don't be afraid to bribe/bug admin.