[CGuenther]

Our team will be using spray paint as well, although our other option was to use iron-on fusable fabric adhesive.

If stability is your main concern, you can find sheets of fabric adhesive at most craft or fabric stores (one main brand is called Heat N' Bond, or it can also be called "fusable webbing"). Sewing the edges of the cut-out numbers in a matching thread in addition to using the fabric adhesive should be more than enough to hold the numbers.