I do not know about platinum, but Pd and definitely Rh form "alloys" with carbon. Palladium melted in graphite is dark in colour. Few times, our PGM alloys melted in graphite crucibles sticked to the walls and they needed to be chisled out - so yeah, carbides are real
All in all, without vacuum furnance you will likely obtain metal foam.
I had good experience with melting in quartz dish in induction furnance. Foam as expected, but allright for selling. As long you do not "switch" to the reducing enviroment (eg touch/stir with graphite rod, blow oxy/fuel flame over or pour it into the graphite mold), you will obtain relatively nice - altough foamy - button. It also tend to spit when you do this