Adding an extra binding works so long as it doesn't look like you have needed to add that extra to make it big enough. That is important, and something judges would look at. Agree totally about putting it in the exhibit. Ashibut - re. your's being 1 inch too small on each side. This sounds like an extra border, 1" wide finished, is needed. After all the hard work you have put into your work, why wouldn't you do this to make it the right size for the Challenge. You still have plenty of time.
I've just realized that mine is a bit too narrow, too... I would need to add 1" to each side. Do I understand correctly that I need to do this only if I intend to enter it in the exhibition? If I don't do that, what happens with the quilt then... I just send it to my partner and that's that????
Why don't you add an extra quarter inch all around in a contrasting fabric. No need to remove the current binding, Cut a 2.5 inch strip, fold RS together, stitch long edge, turn through, press and stitch from the wrong side onto your quilt. That way you will have two bindings! You must put it in the exhibit, that's what it's all about, sharing our work with friends.
Why wouldn't you want to put it in the exhibit?! You could take the binding off and make the binding 1/4" wider, that would make the quilt end up at 18" x 24". You would need to put a little extra batting in the extra bit of binding otherwise it will be too flat - a bit of a fiddle, but do-able, though with that size quilt a wider binding is not as appropriate.