The invitation i) is inherent of the purpouse, altough is totally acceptable only with coworkers. If I want to brainstorm a startup idea with random friends, this invitation may bother my friends - even if they get that they don't need to answer immediately.
The invitation ii) is not inherent, is marketing. It is a barrier to share. You must have good, cool, smart way to introduce the invited people to the tool. Your copywriting will make a lot of differencehere.
You can note that both problems are solved if the tool is already a feature inside a team management tool - only coworkers and using a tool they already know.
ABout the nudges, I guess you have to find just the right time to use them, and also work hard in making it attractive to users, so they want to "play with it".
And about the "async", actually I used the word wrongly. What I am, the tool must keep the chronological order of a brainstorm, in order to one improve each other idea. But the advantage here is that it allows people do it remotely and free from a time restriction. I will read all the ideas there are coming, but I will send mine whenever I choose to. It still a conversation, but it allows more intermissions than a face-to-face meeting.