I think the demo on the landing page should be in the form of meeting minutes, rather than someone messaging a load of tasks to their (I assume) direct reports.

Why? Because the feeling the demo evoked for me was: "Uh oh. This looks like a micro-managers wet dream".

So rather than just have "@John please !phone client" perhaps the demo would itemise the meeting minutes with: "@John said he would !phone client and discuss requirements".

Perhaps this is simply because I have had the unpleasant experience of working for panic-driven micromanagers before. But I think you really want to make sure your landing page is resonating with "Awesome - this is going to make my life easier" vs. "What pandora's box of hell will this tool unleash in my organization and work life".

Product definitely looks useful though, and the above comments are about making sure you present it in its best light. Good luck!