Disclaimer: I don't have an Xbox. I also don't have any experience with European devices and video formats.
I did a cursory search on this earlier this week for my own edification which concluded PAL60/PAL50 conversion devices are available and would solve your issue if the video format source to the monitor was the only problem and/or the monitor could handle either format. But, by your own post the Xbox 360 will not play PAL50 games for whatever reason, so the problem would seem to lie there. If that's the case, then no monitor connection voodoo will change that. This
Xbox 360 PAL50/60 Option... ? and
Xbox 360 - Support - Troubleshooting FAQ for Games discuss changing PAL display settings on the Xbox itself, perhaps that's all that is required. Have you memorized the manual or called Xbox 360 support? I would think this would be a common issue.