I’ve done full fare last minute parallel bookings during service meltdowns several times, when the lines and the phones look hopeless. Delta has always refunded them. In the end, you fix it when going by the boarding pass scanner — they have to fix it then.
My suggestion is to get a printed BP when there is even a HINT of schedule or weather trouble for a flight. Then when you board an alternate flight you have the printed BP for your original trip and the parallel booking on your phone, so the agents can see both at once. (Also helps to show what seat you had when they suddenly reseat you or there is a mystery seat duplication or the flight attendant starts moving people around on a delayed flight before it is scrubbed and you all deplane.) And if you are in a gate area or sitting on a delayed plane, plug in immediately — have had situations where I am using the last 2% of charge trying to stay on hold or check status, rebook, whatever.