Washing + Pink Bean

That's a pretty bad estimation of what mages have. According to this:

at level 30, the minimum amount of HP a mage has is 364. Assuming this mage gains an average of 12 HP per level, that means at level 180, a mage has 2164 HP already. Add a MoN and a Master Adventuer Medal and that mage will have 2664 HP. Add HB and that mage has 4262 HP. That's enough to survive 4262 x 5 = 21310 damage. If that's not enough, level the mage to 200 and the mage will have 4646 HP with HB. That's enough to survive 23232 damage, well over the requirement for Pink Bean.

You're a bad estimation!

I purposely didn't add MoNs because KMS doesn't have them and gMS being able to survive PB is not the issue here. Otherwise, I followed what you quoted perfectly and am well aware that a MoN will add an extra 460 HP with HB.