You realize that its 750km and 7, maybe 8 hours by car? Plus border crossing time (Croatia is not in Schengen). If i were going to hire someone i would first call Laszlo Markus: http://www.silverwings.hu/ We have used him a number of times over the years and he is about the best at what he does. But I suspect that it will cost close to $1,500.
When i get faced with something like this i look for a place in between and fly. Budapest to Belgrade, spend a night or two, then on to split for instance. Probably about $300 in non-stop air fare. Or Budapest to Vienna to Split. $25 for the train and a couple hundred for the flight.