Here are some ideas, all of which have some expense:
Remote Desktop. Set up VNC or another remoting solution. The guest may be another iMac (similar monitor but doesn't need to be as powerful), or a far cheaper PC with the monitor size you want. The OS doesn't need to be the same, and while it's in full screen you won't see the difference. Use whatever keyboard/mouse you want.
Long-range Second Monitor Mirroring, and wireless keyboard/mouse. Lay a long video cable (probably needs a long-range setup or drilling through the wall). Set up the iMac for mirroring. When you walk to the second room, turn on the projector or monitor in the second room, and you see your desktop mirrored. Long-range wireless keyboard/mouse required.
ANY OPTION WHICH INVOLVES MOVING THE IMAC IS EXPENSIVE AND DANGEROUS. But if an executive came to me and wanted me to make such a setup, the minimum would be : Heavy Rolling Table, with a heavily-protected and reeled power cord screwed into the bottom of the tabletop. Drill a hole through the table to pass the iMac power cable through. Multi-outlet Uninterruptible Power Supply screwed into the bottom or leg of the table with many screws, with audible alarm and a large battery. The iMac itself must be securely attached to the table - perhaps gimmick up something to hold the base down. Make sure that there is slack in every power cord, and that no power cord bears tension except the reel which is made for it.
Assumptions on my part: I'm assuming you aren't using Ethernet for network, or cables for keyboard/mouse. I'm assuming your floor is flat and your doors and archways are large. I'm assuming you have the strength to move a table without trouble.
All options which involve moving the iMac will give you grief someday. At some point, you will trip, the power will come undone, the iMac will topple, and you will be very sad. It might still be functional, or it might require you to recreate the entire setup on an entire new, very expensive iMac.