How are the maps provided with Diplomacy supposed to be used?
Make copies of the map (it's expressly authorized) but you'll find most folks won't write on them.  The pattern I see in both home and tournament play is that during adjudication everyone will write down the units they have down the left side of what will become their order sheet.  During negotiations they'll consult their list and look at the map, often indicating moves by tapping their pencil at the start and end of the move their discussing.  Once they're ready to write orders their turn their inventory list into their orders and submit it.

My larger piece of advice is to keep the pace of the game as fast as you can.  Start the negotiation timer as soon as the previous turn has been adjudicated (don't let everyone take time outside of negotiation to write their units).  Similarly, don't give separate time to write orders after negotiation is done -- that's something you do during negotiation and if you don't get them done your units are in civil disorder.  Along those lines be sure to enforce the "no negotiation during builds