"capable of doing virtually everything Thunderbird, etc. can -- and in some cases more"
Dude, just no. Don't be one of those founders. Don't get drunk off your own Koolaid. I'm a heavy daily thunderbird user with 10 accounts and at this point in time, with this release, Thunderbird literally does everything better than Inky. Everything. From account setup, to available options, to information density, plugins, sorting collumn options, UI and collumn flexibility, customization, massive options, and about 35 other things. Email is broken not because it isn't pretty, it's broken because there's too much email, too much spam, and a lack of good threading. Common let's be honest, you made email pretty. You mac-afied it. Took out Spam filter and replaced it with Relevant/Not Relevant.
Your design, name, logo, URL are amazing.
However, Inky couldn't connect to my custom domain inboxes like firstname.lastname@example.org and hangs on the "discover settings" page even after I specify the pop and smtp settings. Gmail works fine though. I'm sure you'll fix that quick so I'm not judging you on it.
Also, Inky has a bad case of the "looks over functionality" flu and "hide everything off the screen and call it minimalization" disease that's been going around. Information density is really low. Every message takes up too much space. With thunderbird my inbox fills up my whole monitor and I could skim through my entire inbox in 15 seconds. With Inky every little message takes up so much visual room it takes forever to check my mail. And everything takes more clicks than usual to complete. And clickable icons like checkboxes etc... are too small.
Not to mention, where is the spam button?
If you sing on your own merrits you'll always find fans, but when you compare yourself to Whitney Houston you're just asking for a backlash. Likewise, had you not compared Inky to Thunderbird you would have been fine.
It is the pervading law of all things organic and inorganic,
Of all things physical and metaphysical,
Of all things human and all things super-human,
Of all true manifestations of the head,
Of the heart, of the soul,
That the life is recognizable in its expression,
*That form ever follows function*. This is the law. 
Also styles and fads like "minimalism" and "flat design" are forms that do not follow function but are really forms that enforce function. Which is why they're fads and go away after enough people jump on the bandwagon and realize the fad's flaw and limitations.