@Eric Mcginn,
You have a good idea and end goal. Just a matter of putting it together. @Nick Belsky gave you great advice.
In this situation, best to keep it as simple as possible, and I often give two offers; first, perhaps an all cash (way below market) and let the owner know that it is what it is--a below-market offer.
#2 would be the seller holds the financing--I wouldn't go to a 30-year amortization, especially with an 80-year-old seller. Perhaps try payments of $XXX with a balloon in 5 years (or longer if she'd like).
You could point out that since it's a rental for the last 12 years, she will have some serious capital gains to pay with a regular bank-financed sale, and with your proposal, that tax will only come due after the balloon payment. NOTE: there may be some tax on interest or principal on the payments--seek professional advice.
Also, stress there will be no inspections or other contingencies--sell the 'peace of mind' side of the equation.
You have known each other for 12 years and you established you are a great payer. I'd play that aspect up.
Best of luck with this one!