It's not entirely impossible to use the MS Wavetable Synth with ASIO drivers. Some, but not all, interfaces do indeed recognize it as as external hardware device.
My old E-MU0404 could see it, as does my Akai EIE Pro. It looks like the 2i2 can see it as well.
Deselect it as the MIDI output device. You don't need it, and it is most likely the cause of your sync problems.
ASIO latency settings do not affect the latency from the MS Wavetable synth. It is subject to the default latency of your built-in sound card (probably 250ms or more).
From the outset of your project, you can use TTS-1 to play your imported GM2 MIDI files. It will be synced to your project settings, unlike the MS Wavetable synth.
The problem here is that you are using two drastically different time references.
Get the MS Wavetable synth out of the picture, and you will be using only one. Moving forward, you should be good to go.
Also, the Audio metronome is fine. It's really just a dedicated synth, and it's easy to get along with.