Ideas for a script for Greenlandic?

I was thinking about what Trump said about annexing Greenland and I was wondering if it would be cool for Greenlandic to have its own script. I don't think the Roman-based script it has right now serves it well, since many words end up becoming very long and cumbersome as shown in this image from Wikipedia:

Comparison of Danish (Top) and Greenlandic (Bottom)

Perhaps a logograph would work better for Greenlandic, as it is a very synthetic and agglutinative language; One symbol could represent a specific word part, such as the part for grass or a grammatical ending. What do y'all think?