When I initially looked at the page (it was after hours for me, and I took only a brief look), you were using the Default Card template. I see you have switched, but I would still like to take the opportunity to provide the answer.
The Default Card template content is more or less balanced between the two sides. This would have been more apparent if you were utilizing more fields in Connections.
With the fields you are using, I can see why you wish to make changes. The only way to accomplish this would be to use a custom template override file.
If you would like to explore the possibility of utilizing a custom template override file, here’s a link to the developer doc:
Template override files can be applied to any Connections template, the included template, and the premium templates.
I hope I have answered your question clearly and thoroughly. Please let me know.
