After trying a number of different solutions from threads on here and others, I seem to have found a configuration that worked. I thought I would share this for other people to try so they can get this fantastic game running well on Windows 7 - 64 Bit (Though I recommend trying it for other versions of windows too).

My setup is as follows:
- Windows 7 - 64 Bit
- Myst Masterpiece Edition (GOG Version - 26573027)
Compatibility Settings - "Disable Visual Themes", Display scaling on high DPI", "Run as admin" checked.
- Quicktime 7.7.9 (Search on Google)
A guide for how to change the below can be found here on GOG in the support section under "crashing video playback issues or other visual glitches"
Control Panel - Quicktime - Settings
Video - "Safe mode (GDI only)" (See Attached Image)
Audio - "Safe mode (waveOut only)" (See Attached Image)
I had also set "Sound Out" "Rate" to "192 kHz" and "Size" to "24 bit", but these probably didn't impact the end result.
Compatibility on "QuickTimePlayer.exe" set to "Windows 98 / Windows Me"

I managed to play all the way through the game almost flawlessly. I did have one crash to desktop but once restarting it and restoring my savegame, it did not happen again. Hopefully this fix works for you! :D

My thanks goes out to the users on this forum and others that had worked hard trying to find a fix, huge credit is due to those that suggested the above. This is just a combination of other user's fixes that seemed to work for me from start to finish.

Also, I would post links but it will not allow me, so I have instead added notes.