I figured out a good solution. Here it is:
In /mail/html/order_invoice.tpl change the following
Code:
{$lng.lbl_payment_method}:
{$order.payment_method}
to
Code:
{$lng.lbl_payment_method}:
{$order.payment_method|truncate:18:""}
You can adjust the truncate value as you wish but I found that 18 was a good value because it allows all payment names up to 18 characters long to be fully shown on the email but when a name like Credit Card (AuthorizeNet: AIM) is used it will only show the words 'Credit Card'
Using the truncate command with :"" after it as above will round to the nearest full word so that you will not get partial words listed on your invoice.