Did anyone find a solution to this issue?
Nope. This problem has been around for years, and they're not going to fix it.
I have not had any problems managing fonts but I use a font manager. I also make extensive use of Live Type and that works very well.
In my experience corrupted or poorly designed and executed fonto are usually the culprit when you can't seem to find them in Adobe apps.
Since version 1.5 of AE, I've only had fonts go missing if something was done that broke the link to the font.
Sounds like you need to take a look at what's happening in your workflow or on your workstation to break the font dependency.
Is the version of Oswald that was used the last time that the project file was open the same as the version that is currently installed? For example, was a Postscript version used originally and now only a TrueType is installed? That one is pretty common.
Rick's recommendation of a font manager is an excellent one. Mac OS X's Font Book is pretty good (not sure what you mean by "inconsistent solutions" as Font Book is a standard font management tool and as straight forward as it gets for managing large numbers of fonts). There's also Suitcase and Universal Type Client.
Of course, as a Creative Cloud user, you could also just stick with Adobe TypeKit fonts. If at any time the link is broken, you can resolve it immediately (see File > Add Fonts from typeset... inside of AE for more).