What are some tricks that you have used to successfully gather feedback from Facebook groups/Other Communities without getting banned?
Most of the communities (your potential customers are part of) usually have rules against self-promotion, product promotions, etc. One of the ways to reach them and indirectly tell them about your product could be via content marketing.
Something along the lines of "come for the content, stay for getting your problem solved"
What are some other strategies you folks have seen or used?
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The easiest way to do so is to provide value. Do you have a new blog post that will help them? Link your blog post - people will be liking and retweeting this in no time if it's actually valuable to them.
After your users are on your site, you can have CTAs or other ways of collecting feedback. I created shoutshare.io for this exact purpose - a small widget pops up, asking your users targeted questions.
I tried the widget on your homepage. Is it possible to collect emails along with feedback from your widget?
Yes! I actually pushed that feature earlier today. Give the widget on the homepage another try - now, after submitting feedback it’ll prompt you for your email.
If a user is already logged in to your site you can attach the email address to any feedback they submit, so this is really for non-logged-in users.
Nice, it works :)
They do because they don't want to get spammed to death. They want to introduce a certain "barrier to entry" so people contribute (and not spam). It's very hard to give general advice because it depends from group to group. I've seen posts where someone does a short 10-15 second demo with a message: "Hey guys, I made a small tool to find niche competitors, comment if you want to try it on", or "Hey guys, made this small tool to find niche competitors, and looking for ways to test it. Tell me what your product is about and I'll reply with your biggest 3 competitors".
I don't think an admin will mind if you use your product to deliver value to his group (in a way where it gets more engaging).
I think answering questions and contributing to the community before self-promotion is key. However I do think some of these communities are being way too strict. If you need any feedback, you can ask me directly on https://twitter.com/nickverhaege.