Please don't use that tool; it often counts wrong. Use bahn.com to make a plan with timetables and then count your travel days.

Also note that Barcelona-Rome is a very long journey. You could use a night train on part of the journey, or use a night ferry Barcelona-Civitavecchia (close to Rome) instead, with a pass discount.

Barcelona - Rome is indeed impossible to do on one day. You could take the night train from Turin but you'd have to pay 57€ in seat reservations to get there…

I'd recommend a night somewhere around Nice or somewhere in the middle but then you'd need a 5-day pass.

I don't know your travel dates but here's some advice about seat reservations.

Madrid - Barcelona can't be booked online but you can go to a ticket counter as soon as you arrive in the country. Here are other ways to book but don't worry availability is generally not a problem as there are trains every 30 min : https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105/index2.html?postid=18419#post18419

The TGV out of Barcelona is very popular so book well in advance (27€ seat reservation). RENFE just restarted a direct train to Marseille from 28th July but it is not yet known whether they accept passes (I've contacted them). This train would be very helpful.

Or there's the ferry (no need to use a pass day for that).

Rome - Paris : 13€ + 30€ with the direct train from Milan OR 13€ + 10-20€ if you take the scenic route via Switzerland ! Let me know for advice :)

Paris - Stuttgart is also quite popular (17€ seat reservation).