First some product advice: You're trying to replace various more specialized tools with a general purpose tool. For example, I use Slack, Front, and Lever in addition to gmail, for internal, external, and recruiting-related conversations respectively. You should explain clearly how your one tool will be better than a combination of the many special-purpose tools.

If you can support yourselves with only 15% time on the old project, that's pretty good. You can probably get Missive off the ground with 85%. Once it's off the ground, it should be easy to get investment to focus on it full-time.

I like to think that investors aren't just a time sink, but can give useful advice about the parts of the business that are common to the other businesses they work with, like customer acquisition, hiring, and managing teams.