Because you will be traveling mid-September to mid-October, I strongly recommend visiting Andalucia on this trip. Andalucia is very very HOT during the summer months so autumn is the perfect time to visit. Seville could still be hot, but if you are there in October, it might not be too bad. We visited Madrid, Toledo, and Andalucia from mid-September to October 3 in 2017. It was in the 80's in all our destinations, except for Seville, where it was 90 - 95 at end of September/very early October. I've heard that temps during the summer months can be 100F or more!
I agree with Maria that if you haven't purchased airline tickets yet, you should fly home from Lisbon, if that is your furthest destination. That way you don't have to backtrack to Barcelona, which is time-consuming.
And I agree with Laura that if you have booked flights home from Barcelona, then consider flying from Paris to Lisbon, and then make your way to Barcelona so that you end up there.
In four weeks, I believe you do have the time to visit the places that Maria suggests. I have been to all of those places, so this is a proposed itinerary for you (i'll assume you are starting out in Barcelona, which is your original plan):
Barcelona - 6 nights
Then take AVE train to Madrid
Madrid - 4 nights
Then take train to Toledo (30 minute train ride)
Toledo - 2 nights
Then take train to Cordoba. You have to change trains at Atocha in Madrid.
Cordoba - 3 nights
Then take ALSA bus to Granada.
Granada - 3 nights
Then take ALSA bus to Seville
Seville - 4 nights
Then fly from Seville to Lisbon
Lisbon - 4 or 5 nights (depends on whether or not you can fly home from Lisbon)
5 nights will give you time for a day trip to Sintra.
If 4 nights in Lisbon, then fly from Lisbon to Barcelona for the last night of your trip. It would be better, though, if you don't have to be in Barcelona twice.
I don't think this itinerary will be rushed because you don't have any one-nighters, and only one 2-night stay.
And you don't really lose a whole day traveling. We took morning trains and buses. For example, we arrived in Cordoba in the early afternoon. After checking into our hotel, we had lunch and then visited the Mezquita around 3:30PM. We had similar situations for Granada and Seville, where we had time for lunch on our arrival day and a little bit of sightseeing or just wandering around the neighborhoods.
Oh, the ALSA bus is wonderful. They are modern, clean, comfortable, and air-conditioned. On one ride, they distributed bags filled with snacks and a bottle of water to each passenger!
Hope this helps.