Hi Susan,
You're taking the long way home. Seriously, if this invoice is going to be a regular occurrence, get and install Adagio Multi-currency. This is the easiest and best solution. This should be your first choice unless this is clearly a "one off" single invoice situation.
If this is a one off situation, simply create a new AR control account for USD customer(s) and simply leave in "Par" dollars in OE and AR. After posting the invoice and retrieving into AR, adjust your AR GL balance with the exchange with the offset being sales if the balance is outstanding over month-end. If not (ie. paid in the same invoiced fiscal period), just deposit the cash into your USD bank account when paid, and adjust your GL bank account for the exchange pickup and credit your sales. Your sales analysis will be incorrect with this workaround, but it is simply an alternative solution.
Adagio Multi-currency should fall into "Best Practices", if you are either buying product for inventory or incurring expenses in another currency other than your domicile country, or if you are selling into another country with a different currency. Multi-currency isn't just a good solution, it is an outstanding Adagio solution that more people should be considering if they want an easy way to manage multi-currency transactions for effective financial reporting.
Best,
Brian