Currently if Succumbing-Song Morganite is active and you reflect damage, it is doubled. This should not be the case, since your monster isn’t really “dealing” the battle damage just changing who takes it.
here’s an OCG ruling that should also apply to TCG since we also follow the same 10 steps to determine battle damage.
https://db.ygoresources.com/qa#24087
01: This card inflicts double battle damage.
02: Battle damage is taken by both players.
03: Battle damage you take is also inflicted to your opponent / your opponent takes any battle damage you would take instead.
04: Battle damage is treated as effect damage.
05: The player gains Life Points instead of taking battle damage.
06: Battle damage becomes 0.
07: Battle damage is halved.
08: Battle damage is doubled.
09: Battle damage becomes X (X being a predetermined value).
10: You do not take battle damage if it is more or less than X.
(However, note that if the Battle Damage has become 0 when applying “06” effects, the remaining effects are not applied.)