Glass can't be easily reshaped. The sort of situation you describe is something that should only happen to you once, anyway.
Yes, it can be. If you were dealing with modern glass you'd lose some quality, but Dwarf Fortress green glass is not going to lose a meaningful amount.
In the ancient world, the fact that glass could be easily melted down and reshaped was a major part of the glass industry -- in Rome, for instance, most of the empire's glass was made in a few centralized locations, formed into large blocks, then sent out to be melted and reshaped elsewhere. There were also people who would collect broken glass objects and 'recycle' them by melting them down and remaking them (and we still do that today.)
Glass is one of the easiest materials to recycle, and with very little loss of material. You couldn't do it with, say, a high-quality modern glass window, say (not if you want to end up with something equally high quality), but with glass bottles, or a lump of raw glass, or a big solid block of glass? Sure.
But more importantly, I mentioned elsewhere that you ought to be able to order glass blocks from merchants, then melt them down and turn them into whatever you want; this would let you craft glass on a map with no sand. Historically, that is actually how glass-crafting worked for much of history (whereas importing sand didn't generally happen at all.) In fact, this malleable nature is part of what made glass so useful to the ancient world -- they used opaque glass the same way we use plastic today.