I question whether that box is rated for a heavy fan, or really whether it is fan rated at all. The ears the supporting bolts would thread into would probably carry the load of a modern lighter duty fan (e.g., modern Hunter) but would the threads hold? You would also need screws/bolts rated to carry this load.
The bar would probably support a medium duty fan and you should be able to just replace the box with a truly fan rated one. The fan rated boxes usually have a greater depth of female threads for each of the two screws/bolts to thread into, not just 1/8" thick tabs.
How high off the floor is this? How capable are you working on a tall step ladder. (At age 80 I think about falls.)
What brand of fan do you have? The tape measure obscures the fan support bracket. I have installed a number of Hunter fans, both the old oil bath heavy fans (decades ago) and more recently the new light weight ball bearing ones.
The new Hunter fans are designed so they can be installed off-center of the box and directly into a ceiling joist. If the electrical box is adjacent to the joist. the large fan shroud covers the box. The fan is not supported by the box but directly by the joist. The Hunter parts package came with special wood screws with washers rated for this.
Of course if the joist is not centered in the room then the fan would not be centered. Look at the instructions for your fan. I installed some of these fans slightly off the exact center of large rooms and it did not show, but if this is a narrow foyer, then it might be more important to get the fan exactly centered.
3-9/16" - 1/2"
apart, or3-1/16"
. Granted, that's a bit snug considering the screw diameter, but it's workable.