In all honesty, the reason why everything resets is because the game reloads the room and all the objects in it; noticed how the lag from blood particle effects (as objects at least) is ridiculous? Yeah, that's why you need to reload the room.
It is possible, you just need to recreate the player at the savepoint upon pressing R, checking to see if there's a player already in existence, and if there is one just move it to the savepoint location instead of destroying/creating it. Then you wouldn't have that problem with the music resetting.
As for the death music, you can just cut that out, have it say game over (as an object), and then when you press R respawn the player and destroy the game over object.
The problem with a lot of this though is that some rooms need to be reset, like when you need to run to the right and escape some blades or something coming behind you. If you die then, you'd have to check the room and reset the room or just the player accordingly so you don't get stuck behind things.