Right now it seems that for every new instance of Event Calendar I have to go to the module preferences and change the template in that little textbox. When I move to a production server, I have to go to the module preferences of the module on my test server to copy/paste the template code out of that textbox because templates are not stored as files.

It would be great, if templates could be stored as HTML and CSS files in a structure like many other modules (e.g. Ventrian News Articles) do it:
\templates\
\templates\myTemplate1\
\templates\myTemplate1\Calendar.html
\templates\myTemplate1\Listing.html
\templates\myTemplate1\Satellite.html
\templates\myTemplatePink\Calendar.html
... etc. ...

This would allow a more easy changing and migrating of templates.

yes, this is a good idea!

however, you can change the default template for your migration or for easy template management.

It is using DNN localization, you can change the template at Admin >> Lanuages >> nivagate from left side, find DesktopModules/EventsCalendar/LocalResources/Template.ascx,

You can find many default templates are stored there.

We maybe adding more features to make the template configuration process easier in the future release...

This would be really helpful to me as well. I am finding many places to use this module on my web site. I'd like to be able to easily transfer my whole set of templates to multiple instances of the module easily.

Will take note of that in future development.