Barcelona Itinerary Timing

On Tuesday you can do the Sant Pau modernista site (Recinto Modernista de Sant Pau) in the afternoon. You can walk right up and buy a ticket, so no need to worry about the timing. It's a multi-building site (a former hospital), so it takes some time to see.

I don't know what to tell you about Monday. The first two stops absolutely call for purchasing tickets in advance. If you don't have one of the first time slots, you may not get inside at the official ticketed time, because they seem to allow people to enter only as others leave. They are both really crowded (Casa Batllo being worse for me in 2016), and I suspect the metered entries are a matter of safety (dictated by the fire marshal?); they were doing it prior to the pandemic. Another difficulty is that at the time of my visit there was an interesting display about Gaudi's other buildings at Casa Mila. I spent a lot of time there, because I'm nuts for modernista architecture. I don't know whether that was a temporary or a permanent exhibition.

If you go to Casa Mila first, I'd suggest at least a 2-1/2 hour gap between the ticket times. That will probably be more than you need, but you can walk around the Eixample in the meantime. The two buildings are a few blocks apart.

On Thursday you could take the Barri Gotic walking tour offered by the tourist office and then supplement it with the non-overlapping part of Rick's walk (if any) and more wandering. You should at least walk by the Palau de la Musica Catalan to see the exterior. The tours there are good, but the English tours sometimes sell out, so that needs to be booked a bit in advance to be sure of scoring a ticket. Another option is to attend a performance there.

Thank you for some other ideas! Exactly what I was looking for. Do you think I should move casa batllo to another day so that I can get an early timed entry for that as well? Maybe Thursday or Saturday? The only thing that’s set in stone right now is the Dali day, so I could move days around as well.

I’m also going to Barcelona in September and plan to schedule the popular sites ( Sagrada Familia, Casas Battlo/Mila, Parc Guell) for first time slot when they open. Barcelona receives the most cruise ship passengers in all of Europe and their numbers can overwhelm the city’s sites from 10am-3pm.
Casa Battlo has an official opening time of 9am for €29. But it also has a “Be the First” admission ticket for €45 that allows entry at 8am that is attractive to visitors like me who are shutterbugs or want some chance of peace & quiet to enjoy this masterpiece before the hordes arrive.
If your arrival Sunday is the first Sunday of the month, there are a number of attractions that have free admission, such as Palau Guell—one of GAUDI’S earliest architectural designs.
I’ve read online in several articles ( don’t know if it’s true) that Parc Guell’s Monument Zone can be visited at 7:30am before the Monument Zone requires admission tickets at 9:30 am when it officially opens.

I think it's an excellent idea to slot one of the sights requiring a timed ticket first thing every morning. That will minimize (or possibly eliminate) the need to guess the best entry times for second-of-the-day sights. It will allow more efficient sightseing, overall.

Heartily second the suggestion of @acraven to visit Recinto Modernista de Sant Pau after seeing Sagrada Familia. We did just that in September, 2019 and it was a highlight of our time in Barcelona. Enjoy!

I did the Sunrise Tour at Casa Mila (La Pedrera) at 8 am, and although it was more expensive, I thought it was great value not only for the much better picture opportunities, but because it was a guided tour with an excellent guide, and you got to see places not otherwise open to the public. The tour took an hour, and then you could spend more time if you wanted, but the tour was very thorough. It seemed like a better value than the 8 am Casa Batllo spots, as those aren't a guided tour.