I'll be the contrarian (as I often am). While a string of 1-nighters is often/usually a poor decision, when you have a car, it's not at all a bad idea.
Days 1-5. Consider going straight to Sintra for 2 nights. It's as easy to get there from the airport as the center of Lisbon. Take Uber (cheap) or a taxi (not quite as cheap) to and from Sintra. It's much better as an overnight stay. I loved spending a relaxing half day in Cascais.
Day 6 - there are 2 possible "excursions" - cork factory and megaliths. I chose the Corticarte Em Arte cork factory tour and found it very interesting, they also have a shop with a wide selection of quality products at good prices. It's about a 1/2 drive from Evora.
Day 7 - Obidos either early or late. The walled city is small and is often crowded with tours from mid-morning to mid-afternoon. I saw Batalha and Alcobaca on separate days, but you could easily see both in one day with a car. I'd allow about 2 hours for each. That should also give you time for Obidos in the morning if you get an early start. Or maybe stop in Obidos late afternoon on the way from Evora to San Martinho.
Day 8 - The RS walk is very good and the fado performance near the end of the walk was enjoyable and educational.
Days 9-10. I spent 2 nights at Quinta de Maroccos just outside Regua. Wonderful! dinners were great, wine was excellent.
Days 11-14. You do not want to have a car in Porto. Best is to return the car at the airport and take the metro to the city. Guimaraes and Braga are possible as a day trip from Regua, or leave early on your last day and see them before dropping the car.
I liked both Tomar and Aveiro, but my trip was 9 days longer than yours. I think you've chosen well.
Car rental. Take the toll reader option. It is well worth the time (and trouble) saved. I used Europcar and booked the rental 3-4 months in advance. For some reason, I went back a month or so before my trip to check prices and they had dropped considerably. I ended up booking and cancelling several times before I got the best price just a couple weeks ahead. I was planning to schlep out to the airport to save €50, but then the price from Oriente station in town dropped and the price difference was negligible. It was easy to drive out of Lisbon around 11 am. Even in morning rush hour it probably would have been okay, since most of the a.m. traffic is into Lisbon. I brought my own Garmin and had some trouble with routes, ended up comparing it to google maps often. Also pick up a Central Portugal paper map at a TI, it will help as well.