Whether or not the boards were structural way back when, they are structural now because the concrete was poured on top of them.
Put up temporary joists paralleling the existing joists then tear down a strip of old ceiling at a time between two joists. Replace with new permanent joists. with short subfloor planks spanning two new joists at a time center to center.
I would anticipate that, due to the weight of the concrete, the new joists would have to be put at less than 16 inch centers. Consult the International Building Code or similar code book used by your city to figure out the joist size and quantity needed to meet the pounds per squre foot floor loading for new framing plus the weight of the concrete given the latter's thickness.
You might also need a center beam where none was before, to support the weight of the concrete and to better install half length new joists where a full length joist could not be wiggled into place between the walls.
Was this room converted to a fallout shelter at some earlier date to justify the concrete on top?