Would it be possible to make it a little more black and white than orange?
Sure, but the APR is neither black nor white--it's a blend.
Whether paid in cash or financed it is still a finance charge
If "it" includes the interest and the fee (PFC), I agree.
Yes, if you're paying yourself the fee out of the loan proceeds or collecting it in cash.
Why would it cost the customer more over the loan term to pay the fee in cash?
It doesn't cost more if the fee is paid in cash. In your example, the deal with the fee paid in cash has a Finance Charge of $1,259.05. If the fee is "financed", the Finance Charge grows to $1,281.75 --it costs $22.70 more to "finance the fee."
That's what the APR is stating correct?
No. The Finance Charge is the cost in dollars. The APR is your yield--and it is a blend, reflecting the two types of Finance Charges you are using in the pricing of these loans.
If you provide the remaining input for your two examples (interest rate(s) and dates/amounts of the two payment schedules), I'll be happy to give you a more specific explanation.