The price difference is not so much if you take the 7.00 am EI flight on 27th and return on the EI evening flight. -about 300 total more than FR flights.
If you take the EI pm flight out on the 27th and the EI earlier flight home on the 30th then ,yes, the difference is enormous .But it's far better to take an early flight out and a late flight back so that you get much more time in Rome.
It would be sad to arrive on the 27th in dark and basically go straight to a hotel. Just as it would be a pity to leave early on the 30th. That'd would only give you two days in Rome yet three nights costly hotel.
So, my advice book EI.
If there are organised pilgrimage-packages at that time with Joe Walsh Tours or other pilgrimage companies I don't know. Check them out .
I must be blunt .If I was still a travel agent i would be wary of booking an 86 year old with Alzheimers on such a trip.
Remember that once you book and something happens that prevents your nana from travelling , then it is unlikely that there would be any refund for any one of you as I cannot imagine any travel insurance company covering you.
Likewise, if anything happened in Rome then ,again, I doubt that an insurance company would cover you for costs.
If you do find a deal with a company that is experienced in such travel i.e. elderly/infirm people on pilgrimages then I'd book with them. Any travel agent will tell you who is doing such tours.
But you must tell the travel agent full details of your Nana's condition.
P.S.- most of the package tour hotels in Rome tend to be small with tiny lifts.
Unless the travel agency staff is clever, knowledgeable and caring then you could end up in a hotel that is perfectly fine for 99% of guests but not for your Nana.
P.P.S. Weather can be bright,sunny, albeit cool, at that time in Rome. It can also be cold, wet and windy -a bit like today in Dublin. It gets dark ca. 6 p.m.