Commerce one-off products in admin interface
The line item title in 1.x is derived from the line item type's title callback. Your simplest option is going to be to define a new line item type, as you've surmised, and have its title callback pull the value from a field you add to the line item type and expose to administrators to edit. Alternately you could edit the various Views to render this field directly ... but then you'd still need some way to allow creating ad hoc line items on the back end.

Sorry, I wish it were easier.