Hello from Wisconsin,
We did Budapest to Zagreb and it was a great trip that allowed us to see the countryside and slip along Lake Balaton. Split is good distance further. We eventually took the train on to Split. But only after messing around in Zagreb, Lujbliana, and Slovenia countryside. But I would recommend breaking your train trip with an over night in Zagreb.
dbahn is a great site to find times of trains in and out of just about anywhere in Europe. Be patient with the site, but you can ask for times between places and train changes that are necessary It is possible, though not likely, that Zagreb wouldn't be the best over night location. Seems you will leave from Budapest Keleti station. The searches you make on dbahn will ask for station, not just city. In Zagreb I think the main station, the one you want would be, Zagreb glavni kolodvor. I think that means main station. Glavni is the key. Zagreb has more than one station on the main line. Glavni = main?
Budapest is a great place deserving of days. Split, we spent four days, and it was fine. I think most people would be happy with fewer than four days. But we move around a place slowly. One night we went to a French movie subtitled in Croatian (we don't speak either language)plus an evening performance where the crowd sang along quietly with the performers.
Read up about the history of Split before you go, if you haven't already.