Retrofit Fan box for horizontal 2x4 truss
I would take Ecnerwal's suggestion a bit further. Build some simple blocks with flanges using 2x3 (so they fit through the hole) and plywood (whatever you have on hand). Drop them in place with beads of construction adhesive or wood glue on the backs. Come back a day later and carry on.
SIDE (ELEVATION) VIEW
     ____ ______________________
    |    |                      |
    |----|-------- &lt;--screws    |&lt;-- new 2x3 block
    |    |                      |
   ||----|--------              |
   ||    |______________________|_____ &lt;-- glue joint
   ||    |                            |
 __||    |                            |
   ||    |&lt;-- glue joint              |
 __||    |                            |&lt;-- truss chord
   ||____|____________________________|
       ^-- plywood

TOP (PLAN) VIEW
     ____ ____________________________
    |    |                      |     |
    |    |                      |     |
    |----|--------              |     |
    |    |                      |     |
   ||    |                      |     |
   ||    |                      |     |
___||    |                      |     |
   ||    |                      |     |
___||    |                      |     |
   ||    |                      |     |
   ||    |                      |     |
   ||    |                      |     |
    |    |                      |     |
    |----|--------              |     |
    |    |                      |     |
    |____|______________________|_____|