So I just tested how Regens interact, and the result is completely unexpected.
Gaia: 400/turn, 3 turns
Joan: 250/turn, 3 turns
Used Gaia's on turn 1, then Joan's on turn 2.
Result
T1: 400
T2: 250
T3: 400
T4: 400
I then repeated with the reverse order of skill usage.
T1: 250
T2: 400
T3: 250
T4: 250
This data suggests that Regen does indeed work like debuffs, except Regen doesn't miss; it always extends the previous Regen. BUT the newest Regen effect applies on the current turn, and the current turn only.
I repeated with Yggrdasil's regen (before or after Gaia's) and observed that the regen lasted 2 turns instead of 3 when Yggdrasil was used second. We can thus conclude that the duration of the new effect replaces the duration of the old effect.