Hi Lisa Thanks Greg is on my go to list for future hosting. Out of possible interest to you here's response from our host providers:
Further to your enquiry (170715-000298),
gzip compression will require high resource of the server. Which will affect other websites hosted on the same server. Most likely, this is not possible on our shared platform. However, if you want to optimise your website, you can optimise your scripts instead to lessen the execution time and increase the loading time of your website. Otherwise, you need to migrate a dedicated/Cloud server, or look for a hosting provider that supports gzip on their shared server.
Looks like they really value our custom don't you think!!
Have a great day.