Thanks you for your try !
The beginning is indeed a little too hard, you need to cheat in damaging them and using the seal to capture. Also sleep is too strong as damages doesn't wake the monster. They also have too much moves at low level.
There is only one music in the wild (one by direction would have been nice), the differences is due to the 13 year old web NES emulator I have modified to work on today browsers which give a less powerful NES than other emulators, so you are experiencing some lags in the generation of the tiles and it doesn't have the same number of tiles to generate on vertical and horizontal, this make the music slow down differently. You can test with the downloaded ROM to avoid the lags.