I hate to say this, but I would pretty much skip Las Ramblas altogether unless you want to go into La Bouqeria market (which I do suggest, in which case you can do that stroll fairly quickly from Placa Catalunya). It's very touristy and to be honest, can b ea bit seedy. I completely agree that visiting Montserrat should be reconsidered as there is A LOT in Barcelona to see. With two days in Barcelona proper, I'd spend the first day in the Gothic Quarter and El Born area (located next to each other), which is enough for a whole day and you can make frequent stops to enjoy all the people watching without you feeling like you are sacrificing the limited amount of time you have. Within that area you can visit:
*the Temple d'August (Roman column ruins),
*Santa Maria del Mar (have you read "Cathedral by the Sea?" It's an amazing book and features this church),
*the Picasso Museum,
*several markets: La Boqueria, Santa Catalina market, El Born market (has medieval ruins underneath it),
*the city museum which is very close to the Cathedral, and
*the Chocolate Museum (good for maybe 30 minutes and really, just an excuse to buy a lot of high quality chocolate.
There are tons of wonderful little cafes, bars, restaurants, shops, and markets within these two adjacent neighborhoods plus plenty of places to sit and enjoy people watching. On a Sunday, I think you should see more people out and about because of the churches, but its a really spectacular area. I personally found El Quatre Gats to be a tourist trap, but its worth a drink if you are a fan of Hemingway and others.
As for your second day, I would keep your schedule as you've written since it sounds as if you've got some of that locked in, but I would spend your dinner and evening in Gracia rather than Las Ramblas. Alternatively, the Eixample neighborhood (near Casa Batllo and Casa Mila) has a lot of really nice restaurants to choose from.
Keep in mind that its not uncommon for restaurants to START serving dinner at 9 or 10pm. You will have a hard, but not impossible, time eating before 8pm. The exception of course are the restaurants catering to tourists.
Have a great trip!