I'm still new to this business myself, but I'd argue you might as well give it a shot and contact publishers anyway. If anything, you can show them what the audience for your game looks like already (if people have been downloading/buying your game), and that you've been taking feedback into consideration. Beyond that, you could look into a company like Print and Play to make your own polished prototype. These days, though, it'd likely be more painless to just Kickstart your own small-print run.
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Thanks to the advise, I guess I'll go ahead and contact publishers then. Audience of the game is mostly my family and relatives currently, I could try to increase it a bit. And I guess I can link them to my Trello board or changelog which holds all my iterations to show that I'm actively concidering feedback.
Print and Play also looks very cool, if all else fails I'll just order some copies from there.