Ok, we need to clarify a few things:
1: Is the Xray machine itself connected to the battery backup outlets, or just the surge protected outlets on the UPS?
2: What do you mean by "it kicks on"? Does it go to battery backup, or does it trip and shut down on overload?
If it is just going to battery backup (or online if you prefer) then it sounds like it's doing it's job. The incoming voltage is probably sagging enough to trigger the online mode. There may be a problem with the branch circuit or incoming voltage from the panel/POCO.
If it's shutting down or alarming in overload, then you need to do as you thought and just put the monitor and computer on the UPS and the Xray off of it. If they are all part of the same machine, then make sure you keep the Xray machine on the same circuit or phase as a precaution. (Possible ground loops or grounding issues.) Since you said the load is 1500va and the UPS (by it's model number) is only good for 1200va, I think you will need to separate the Xray from the computer/monitor.
As an afterthought, is the UPS rated for use with medical equipment? Perhaps one of our Code gurus could chime in and say if this set-up needs to comply with the medical equipment provisions of the Code.
