Struggling with this also, but naming solution doesn't work for me.
I've tried specifying the font-family on <body> in CSS. (Which is apparently the proper way to do it; according to Amazon anyway)
I've tried specifying the font: style, variant, weight and family of each on <p>, <i>/<em>, <b>/<strong>.
None working with Moon+ Reader Pro. It only uses the "Regular" font.
It doesn't even work when I attempt to use inline CSS (style=""). Nor even when I create a CSS class and use <whatever class="whatever;"> or <span style="whatever;">.
Whereas, in Calibre and PocketBook, all these methods work.
I should mention these fonts are embedded; there's no "fonts" folder on my Fire HD 8 (yet; want one, unsure where the 'proper' placement is. Main device memory root folder???). And yes, I've heard rumor that there are issues with fonts on Fire HD's (but I can't see how that could be the problem when they DO work in other apps; same device, same fonts).
I've also seen mention about OS/2 type in the font files (apparently, for ADE, only "type 3" is acceptable or some such). Most of the source files were from "type 1"; I did change to "Automatic". And only this font-family is problematic out of over 50 fonts (I have not attempted any other font-family; yet). So it seems unlikely to me that it is anything to do with that. It is font family specific, whatever it is.
Anybody got any ideas? I really like this app best of all (despite its myriad rendering pitfalls if you're trying to go too fancy; definitely not what this one's good for), but... this is not going to do it for me long-haul with this particular, seriously annoying issue.
In a slightly related aside... I'm wondering, what is the proper method (which will work with whatever font you change to) to invoke the true bolditalic font? (When you are specifying the font-family strictly to the <body> tag, not the specific ones per <p>, <i>, etc.)
In Calibre and Pocketbook it seems like it may be:
<strong><i>
<strong><em>
(Know it's not: <b><i>)
Would like to be sure. Thanks.