Once you accept that you will not get coverage on any of the major sites, you can think about how to promote your product. You should have already started before you built anything, to make sure your product solves someone's problem. If it solves even one person's problem well, chances are they will know other people who have the same problem and will be your biggest advocate / promotion avenue.
For promotion, sometimes the old tricks are the best tricks. Yes, ads cost money, but $100 spent on AdSense can still send a lot of people to your site if you spend it wisely.
So don't worry about launching, worry about minimizing your customer acquisition cost. And start by simply advertising so you have an initial cost of acquisition for your estimates.
So my tip is, don't just show the world your product. Show the world what your product can do.
It is best if you can show your product to where people are familiar with. In my case I used Medium, and Reddit. I'm planning to do it to some popular web applications next time.