Just a quick update for anyone that might be following (now or in future)...
I added Contact (as a dropdown) and ContactName (as a linked text field) to the SalesOrder table.
I then dropped the Contact field (the dropdown) on the SalesOrder form, binding the selected value to the ContactName. The Contact dropdown is filtered as follows: "Entity is equal to Screen.Customer_fld".
So now my salesmen can assign a Customer Contact for a SalesOrder. I'll add text boxes for phone and email that will be auto populated with this info when a Contact is selected.
This should give me the functionality I'm looking for.
** Oddly enough, while composing this message I came across the Log Call screen and noticed something very similar to what I will eventually replicate on my SalesOrder and Work Order screens.