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"By linking this billable item to an expense account I believe I've dropped the income portion of the accounting balancing process."
You may know this so forgive me if that's the case but, when you mark an item as billable on a transaction, it just triggers a reminder to add it to the next invoice for that customer. You don't have to keep the expense item on the invoice, you can use whatever item and amount you want so you can choose an income item and mark it up as you want.
"Does this thought process make sense and sound correct?"
Yes.