Both Druid Auto-Attack and Double Punch only procs 1 hit of Aspergillum. Thing is, the bulk of Chaplain’s Auto-Attack damage largely comes from Aspergillum, and Demi Lycan buffs both the physical Auto-Attack and Aspergillum while Double Punch attribute only affects Double Punch damage alone. In the overall picture, Demi Lycan is probably stronger at zero attribute point cost, and affects all damage skills, not just Double Punch.
IMO there’s more than 3 class choices that are viable to help out. For example:
Zealot is probably my recommended pick, gives a huge damage boost that affects both the physical and magic portion of Auto-Attacks, Blind Faith procced by Auto-Attack is counted into Visible Talent damage (easier to cap out Visible Talent damage), Invulnerable allows saving points from Chaplain Paracletus Time (could just go Gazing Golem cards instead) to put it into Deploy Capella, Immolation gives additional fire property damage for Auto-Attacks, and Fanatic Illusion/Emphatic Trust for fire-and-forget damage.
Oracle is just great in Re:Build to give damage boost via Prophecy, damage mitigation skills, Death Sentence to boost damage.
Krivis has fire property damage from Aukuras, Zalciai for party damage support, Melstis if you need buff extending, and Divine Stigma damage support.
In essence, Chaplain is more of a Magic class using Physical Auto-Attacks to proc its damage, and the bulk of the damage comes from Magic Attack.
While Monk provides block penetration, bleed, strike damage and physical skills, the block penetration is too little to matter (unless you’re talking about Palm Strike Hand Knife armor ignore, 7.5% is unnoticeable in damage), bleed damage is not worth talking about in terms of damage (is more about the SP drain), additional strike damage (single target) only affects the physical portion of Auto-Attacks AKA Double Punch and does not affect Aspergillum where the bulk of the damage lies, and those physical skills are a waste of slots assuming Inquisitor is taken (cooldown reset, and Chaplain Auto-Attack is sufficient bossing damage).
Monk is probably only half-decent at best, but the problem is that the other options in the Cleric tree are just that much better and has more synergy outside their respective classes, thus the opinion that Monk is terrible.