I think the plan generally makes sense except it may be expensive to fly from Budapest to Split. I did a random search and the cheapest option involved two stops including Zagreb and the best single stop option appeared to be via Munich.
You have an additional option that may be cheaper and take about as long as the flight experience which is taking the bus, it is about ten hours but many of the flight options are just as long and only get you to Split airport.
If you want more comfortable options, you could spend a night in Zagreb, have a walk and a good meal, then fly to Split the next day from Zagreb. Or maybe even that evening depending on how the schedules work. There will always be Zagreb to Split flights.
You could also spend one night in Plitvice: take the bus Budapest to Zagreb, then Zagreb to Plitvice, spend a night at Hotel Jezero (or a pansion nearby, but the hotel is most convenient on the bus), see the park the next morning, then take afternoon bus to Split.
I never recommend against Plitvice but I am not sure I would take a tour there from Split in March. Upper lakes will probably not be open and weather was an issue there into April this year with snow and ice. If you fly into Split I would recommend Krka instead for your day trip, it is closer and almost as beautiful. If you plan correctly you can do the upper boat tour as well if it is running, which would take the whole day. You just get fewer waterfalls overall - Krka is not quite as popular because the park is much larger than Plitvice whereas Plitvice is all self contained waterfalls. But it is still very popular.
I might also check prices for rental cars from Budapest to Split. My guess is this would be very expensive, you take a look and say, no. Sometimes you will get lucky though. Drive is about seven hours but that would be the easiest way and if you spread it out over two days would let you see Plitvice most easily. If it works there are places to stop along the way as well. You do not need a guided tour for Plitvice, you would just need it for transport really. I walked past a tour this year where guide was - I will not say openly lying, but was completely exaggerating some truths. Plus the tour guides are not likely to be geologists.
I would also do the day trip to Mostar from Split, or depending on bus schedules, or if you hire a driver for more than one day, take a night off of either Split or Dubrovnik and spend it in Mostar. It is just a bit closer to Split.
So in general yes you have a good plan but you may need to be flexible especially with weather.
To get from Split to Dubrovnik first choice in March will be bus as the Split>Dubrovnik ferry generally runs April to October.
Split will not be a ghost town, it may actually be a good time to go.
For Dubrovnik you need one full day to see everything. Buy Dubrovnik pass, pick a day, and do as much as you want to. This gets you on the walls and into most of the worthwhile museums. The maritime museum, pharmacy, and rector's palace are probably the highlights after the city walls.
I would try to find apartments within the central cities/old cities in both Split and Dubrovnik. Look at booking.com for options.
I hope you have a good trip.