Okay! I figured out a workaround. If you go to the folder "Links Awakening DX HD\SaveFiles", and open the text file "saveGame0" in notepad, you can turn on and off different flags in your game's save file. This is assuming the saved game you are playing is the topmost save (which is savegame0, the second save is savegame1, etc.). Make sure you open the text file "saveGame0" and not "save0", which I believe is flags for items instead of events, as well as debug mode (see my note about that at the end for debug mode, which is invincibility!)
Since you're having problems getting past the first level's instrument (which keeps glitching out), you can turn the flag for receiving the first instrument from "off" to "on" this way.
In notepad, go down to the line:
s d1_instrument 0
(I'm assuming the d in d1 stands for dungeon number 1; as you progress through the game, d2_instrument 0 and d3_instrument 0 appear, and so on).
change "s d1_instrument 0" to:
s d1_instrument 1
Then save the file. This should save your game as if you have the instrument. I don't know if this will force the owl to appear as you leave the dungeon or not, but here you go.
I solved my issue with the door in dungeon 7 "Eagles tower" by changing some of the flags from 1 back to 0, or 0 to 1, etc. Eventually I figured out what I needed and turned the flag for the locked stone door on (from 0 to 1) but kept the instrument as unobtained (0) so that when I entered the chamber, the door was open but the instrument was still there.
I hope this helps!
(Note: if you would like to turn on invincibility, then you can do so by opening the other file, "save0" and change
b debugMode False
to:
b debugMode True
...and when you open your save, you won't lose any hearts when you get hit by enemies!)
-Glenn