Stick with 1), with drop down lists, you only see the data entered after you exit the field and its drop down so all that you see in this field will be the Account ID. Now place a readonly copy of the account name field next to this field so that when you select an account ID in the first field, this field displays the name. The alternative, as you've already discovered, is to use a pop up menu. (If your reason for using a drop down is to avoid the "beveled block" look of a pop up, there are ways to format the field to hide that often undesirable 'look'.)
There are at least two layout design tricks that I know of that you can use to hide the ID field and yet still have it function as a drop down list:
1) Use the arrow option with the ID field and then resize it's width until only the arrow is visible. When the user clicks on the arrow, the full two column value list pops out.
2) Place the ID field underneath the name field with a text color that matches the background color. Use the behavior settings in the Inspector to block direct access to the name field. When you click on the read only name field, the Accounit ID field jumps to the front and deploys for the user to select a value.