I know that you state that you are not looking for "workarounds", but I should point this out.
There is indeed not a properly-supported means of doing microtonality within the MIDI specification itself. However, there is an extremely well-established and widely-accepted and implemented system for microtonality with synthesizers and virtual instruments called Scala, and it's easy to use and its microtonal tuning tables are portable and reproducible across many pieces of music software and hardware. Scala supports a myriad of historical tunings and temperaments, as well as avant-garde experimental tunings and any arbitrary tunings you might devise yourself.
Don't wait for the MIDI standard to be upgraded or extended for microtonal scales; people who want and need them have been content to use the Scala system to achieve this instead.
You can read about it at the Scala website.
Here is the Wikipedia article on Scala.
There are many commercial and freeware software virtual instruments that support Scala directly. Examples include Native Instruments, the Garritan Personal Orchestra, and Pianoteq. These products come with libraries of Scala historical temperaments and ethnomusicological tuning tables already available as presets. You don't need to know how to program your own Scala tuning tables to get started, but the Scala system has free software for building your own tunings if you are so inclined, and you can import your own library of Scala tunings into these virtual instruments.
Beyond that, the Scala system includes software that can export Scala tunings (simpler ones of no more than 12 pitches per octave at least) into MIDI specification-format data that can be uploaded into many hardware synths that support the MIDI tuning spec. There is a long list of hardware synths going back to the Yamaha DX7 that support the MIDI tuning spec and will work with the Scala software.
So please don't discount "workarounds"; the Scala system can do what you want.
The Pianoteq virtual instrument digital piano comes with many Scala microtonal tuning tables, or you can import your own Scala files from disk.