How do I provide heating to a room without existing plumbing?
Just go up. The 2 ceilings get a moderate slit for a lot of drilling &amp; short sections of piping with a wall &amp; ceiling corner chunk-out to drop down for the new rads.

And, if the current piping is old then tie in the existing rad to avoid any near-future failures. That piping would be parallel to the joists &amp; you'd just need a chunk-out at the bearing wall &amp; above the existing rad.

Tedious, but gets it done &amp; the ceilings are the easiest to repair compared to everything else.