if you can put a couple of tops together, so all you have to do is the actual quiting......you could use a laphoop to quilt with. have them ready to quilt before you move.
OR keep out a couple of bags of scraps, that you could just cut up, for later use....decide which size squares you want to cut them, then place each different size in a bag or box, when completed.
OR save out a few pieces that could be made into lap quilts or baby quilt tops....and just cut & piece