As a writer, I'd be asking what qualifications you have if you have no testimonials from authors yet.
I also freelance edit, but I freelance for a particular publisher who also specialises in my writing genre (e.g., I edit what I love to read and write).
You could go that way. I'd just recommend making a list of pulishers in your specialist genre, then having a look at their websites for employment positions. Most do ask for 1 year's experience, but if you're prepared to start at intern level and with proofreading, you can work your way up within 6-12 months. With intern posistions, you'll be given tests etc to evaluate your skill level, so it won't matter if you've had little physial experience (your skill will speak for you).
On websites... they are a a very good idea, but you need your experience behind you, and those testionials. I've been paid for freelance content editing for two years now, but I still don't have a website advertising my editorial work (the edits comes via the publisher I freelance for). I still see this time as a building a portfolio period.
To approach an author, you need to be able to convince them that you're worth the money you're asking.
If you approach publishers online, avoid those who mention that payment is royalty-based. That means you only earn money if the novel sells. If you edit a novel and it makes no sales, you don't get a penny for your work. You're after a flat rate: where you're paid in full and on time after an edit is complete.