So sorry to hear about your grandmother. This part of life is never easy.
The quilt is beautiful! Please handquilt it.
I've inherited two quilt tops. One is a whole cloth that's got beautiful embroidery in the middle. The other is all the state flowers. Again hand embroideried. Figured someone has put in all this handwork and it's only fitting I finish them doing the same. Like QuiltnNan's idea using lightweight fusible backing. As I'd think once the quilt is washed, the handpiecing would pull apart.