Under the CD-DVD FORUM, there is a subforum of threads about printers and software for printing on disks.
The packages we use with Epsons, including the one sold with American Epson printers, gives me the ability to define a print-zone and that seems to be all you need. You write about EJECTs and I’m not understanding what is meant by this - it makes it sound like the disk is a bad-fit and the printer is ejecting it without feeding it in.
Or is it ejecting-without-printing because the dimensions or graphics are improperly set? (Which is the likelier cause - the printer could be saying, “You’re telling me to expect THIS kind of disk, but you’ve inserted THAT kind instead - I’m kicking it out instead.”)