Don't they sound natural if the stress is on finishing the work?
I just happen to think that constructions with the -ing form are not particularly common/natural in normal conversation. I remember at school (many
years ago) being taught to use these constructions because they were more 'elegant'. So we used them in our written work, because we didn't want to lose marks, but we didn't, and don't, use them much in normal conversation.
Isn't the second sentence more likely for the given context that work should be finished?
If there is an obligation on us to finish the work, then 'can' is more likely, in my opinion.