Have you ruled out putting the liquid in the bag first, then placing the bag on a baking sheet in the freezer to make the resulting ice block the right shape, then removing your still-clean baking sheet from the freezer?

Then you can pull the bag from the freezer, break off the size of piece you need for a given dish, and stick it back in. If you want the bag contents to be easier to break into precise pieces when frozen, you can place chopsticks under the bag on the tray while it freezes, to make thin spots in the resulting block. And if you use the same size freezer bag for a lot of stuff, keeping the frozen food intact till you're ready to break some off means you can store the bags in a very space-efficient manner, compared to what would happen if you broke up the food before storing it.

It gets the bag dirtier, but it skips the whole step of re-packaging the food once it's frozen.

Similar deal with freezing a sandwich bag of something atop an empty ice cube tray. The frozen liquid ends up block shaped enough to be easy to break apart, but you eliminate the steps of removing frozen food from the ice cube tray, packaging the food, and cleaning the tray.