Suggest reviewing
THIS.
As I understand it, you have VERY high mortality rates (90% +), affecting chickens and turkeys, but seemingly not ducks (or to much less extent).
Onset of symptoms to morbidity is rapid - 5 days +/-
Symptoms include:
Redness and leakage at the eyes.
Sneezing
Lethargy
Weakness
Gaping/Labored Breathing
Green Runny poops
and you have, effectively, no biosecurity. and your ground has been the sight of prior outbreaks.
Green watery poops are common symptom of four diseases:
Marek's
Quail Bronchitis
Chlamydiosis
Mycoplasma
vND (virulent Newcastle Disease) has been in the news lately, and there have been some major world outbreaks. High mortality rates (up to 80% in some versions) fits, as does conjunctivitis, lethargy. But no green poops, it affects all avians, so your ducks would not escape, slower progression, and your symptoms lack the paralysis, trembling, and neck twisting characteristic of the disease. As a not vet with access to the internet, my guess is NOT THIS.
Quail Bronchitis - affects primarily quail - and while the respiratory distress is present, with lowered food water consumption, its not nearly so fatal. and you have the wrong birds. So again, as an "I am NOT a veterinarian", but I do have access to the internet, my guess is NOT THIS.
Chlamydiosis - affects ducks, but rarely chickens. Already doesn't fit. Slow progression through turkeys, rarely affecting more than 50%. Based on those facts alone (there are other reasons it doesn't fit, too) as an "I am NOT a veterinarian", but I do have access to the internet, my guess is NOT THIS.
Marek's is associated with cancerous growths throughout the body. Its a slow progression, usually affecting older birds (you lost chicks), and missing some of the other symptoms. Greenish wet poops present only end stage, as cancerous growths destroy the organs. I am NOT a veterinarian", but I do have access to the internet, my guess is NOT THIS.
AI (Avian Influenza) - highly contagious, can approach 100% mortality, and can move through a flock rapidly. Wet poops are one of the symptoms, not necessarily green. Ducks don't get a pass, you didn't mention blue combs and wattles. Best guess as someone unqualified to do so?? NOT THIS.
That leaves Mycoplasma.
I'll quote from the source linked above:
MYCOPLASMA SYNOVIAE
Synonyms: MS, infectious synovitis, synovitis, silent air sac
Species affected: chickens and turkeys.
Clinical signs: Birds infected with the synovitis form show lameness, followed by lethargy, reluctance to move, swollen joints, stilted gait, loss of weight, and formation of breast blisters. Birds infected with the respiratory form exhibit respiratory distress. Greenish diarrhea is common in dying birds (see Table 1). Clinically, the disease in indistinguishable from MG.
Transmission: MS is transmitted from infected breeder to progeny via the egg. Within a flock, MS is spread by direct contact with infected birds as well as through airborne particles over short distances.
Treatment: Recovery is slow for both respiratory and synovitis forms. Several antibiotics are variably effective. The most effective are tylosin, erthromycin, spectinomycin, lincomycin, and chlorotectracycline. These antibiotics can be given by injection while some can be administered in the feed or drinking water. These treatments are most effective when the antibiotics are injected.
Prevention: Eradication is the best and only sure control. Do not use breeder replacements from flocks that have had MS. The National Poultry Improvement Plan monitors for MS.
There are other forms of Mycoplasma, but this one, I think, best fits, and that only partially - no lameness or breast blisters. MYCOPLASMA GALLISEPTICUM is virtually identical in symptoms, but also affects ducks. Both are highly contageous. What I don't understand is the mortality rate. Near 100% deaths are unheard of. Even 15% is high. Same with the speed of progression thru the flock and rapid mortality. Based on those factors, I'm going to eliminate Mycoplasmosis as well.
...leaving me out of diseases to offer you. I'd look for another cause - likely something they ate but the ducks didn't, possibly while they were at large. That you broody hens, who don't travel far, are also unaffected gives further weight to that theory.