That's going to be a great trip. I did a train and bus trip through those two countries in 2015 but have zero experience driving there.
What is your source for the driving-time estimate between Gura Humorului and Sighisoara? ViaMichelin is giving 7 hr. 21 min. for its fastest suggested route. Although there's a separate thread running right now about the feeling that VM isn't updating its database these days and is probably not a good source for driving directions, I haven't seen any suggestions that its driving times are over-pessimistic. I'd hate for your guesses to be 1/3 short overall. But then again, if you're mostly taking buses, you'll be looking at the official schedules for those.
In any case, Sighisoara is rather small and I think in a pinch 1-1/2 days would probably work there, so if you need to, you could probably drive (or bus, if available) on to Sibiu by mid-afternoon on the third day. Incidentally, the Sighisoara tourist office was closed the day I was there, which was a Monday. I suggest traveling with a map printed off the internet, just in case--not for driving, but for walking around the somewhat tricky historic district.
Two places I saw in Romania that you're going to miss are Timisoara (where the revolution began) and Maramures, the folkloric regions with wooden churches that's north of Cluj-Napoca. I will concede that Timisoara isn't absolutely essential, though I liked it a lot, but to spend as much time as you plan to in Romania and miss Maramures is a real shame. Although I'm usually telling people on the forum that I think they should slow down--and I do not like 2-night stops myself--I'm going to suggest that you try to find a way to get Maramures into your itinerary.
The Retro Hostel in Cluj-Napoca organizes van trips to a number of destinations in Romania. I took its 2-day trip to Maramures and thought it was a great, low-stress way to see the area. I don't think it can be done by public transportation, and I'm pretty sure a self-drive trip would miss quite a lot that we saw. You don't have to be staying at the hostel to take its tours, but the trips only run when there's enough demand, so that can be tricky. Also, my group was in a charming rural B&B-style place with very good, home-grown food, but there were no rooms with en-suite baths: 3 rooms and 2 baths, as I recall. It was absolutely worth it to me.
Where would the time come from? Perhaps by cutting one day each from some combination of Brasov, Sofia and Nessebar--depending on what side-trips you might be planning in each of those places. With a car, I think you can just about squeeze Nessebar and Sozopol into 1-1/2 days. Another possibility is to do what I did and only spend one night in Bucharest. The thing about Bucharest is that there's not a concentrated area of historic architecture--or at least I didn't find one. I did a lot of walking to find some individual buildings of interest, though I'm certain there are museums there that I would have enjoyed if I could have spared the time.
I note, however, that you say you plan a 24-26 day trip, but you have allocated 27 nights. Still, I would do just about anything to get to Maramures.
In case you haven't encountered this information in your reading: As of 2015, some inter-city buses in Romania required reservations, and they had to be made by telephone, not at the bus station counter. Be alert to that when you look at schedules or talk to someone (who may well not be English-speaking) at a bus station. That happened to me twice, but I was able to find folks who would make the telephone call for me.
Be wary of a skilled pair of young male pickpockets who lifted my wallet in Veliko Tarnovo.
If you're into crafts, you'll probably find your best opportunities in Veliko Tarnovo and Plovdiv.