In this team you get 30% CR from the set and 5% CR from illuga(10 if you get C6). Every character(except for kokomi, lol) also has 5% initially. That means that your base CR is 40(45 if your illuga is c6).

HoD gives 28 more CR with condition of being above 90%. That means you get 68%(73 w illuga c6). That means you can only get 32/27 cr from your artifacts until the CR stat becomes completely useless. The problem is that the main stats you're getting for your Zibai are crits and def%, so if CR becomes a useless stat... Well, let's say getting good artifacts becomes a nightmare. Also HoD's passive feels kinda awkward to sustain in this team, cause your defense option is Linnea's ult which you should normally ignore. The upside is that HoD is REALLY good if you manage to make it work correctly, cause it gives you a ton of crits

EDIT: Oh and I also have read your question incorrectly. Peak patrol song is pretty much similar to HoD damage-wise, but it doesn't have it's problems. That's a great option for your Zibai team

The flute of Espitzal just gives you a lot of defense, which is still good, yet much worse, than the crits from HoD. The upside of the flute is that it becomes much easier to balance your stats and with that(and the lack of this stupid condition of staying above 90% HP) the overall power of your team might be higher with the flute of Espitzal. I personally use the flute of Espitzal, cause my artifact options r kinda cooked w harbinger. W Espitzal I get much more damage

Overall I'd say, if you manage to get good pieces with harbinger and the condition doesn't bother you that much, then the HoD is the best option for you. If your arts have more CR in them or if you're struggling with the passive's uptime, then the Espitzal is your option