Will a 6ft. Fence Work?

Have been reading all the messages about chickens missing during the daytime. Same is happening at our farm in Western NY. Never had predator problems before which is probably odd. We saw a coyote last year in our vineyard and I heard a fox calling this Spring, (but didn't see him) other than that we have the usual raccoons, oppossum etc. Have hawks in the past but have not seen one all this summer. Chickens are in a very sturdy sealed henhouse. Auto door shuts at dusk so I'm positive all the abductions are during the day. We have 4ft. welded wire fence around our back yard, hooked to our house which encloses a pond and the henhouse. We also have 3 adult geese, 3 Pekin ducks and 2 male peacocks which all seem to get along. Just in the last two months when this started we have lost 7 adult laying hens (3years old) and 8 young 3 month olds I raised from chicks. They free range in a big fenced back yard that attaches to the house so its weird we have not heard or seen anything!!! I go out several times a day on the deck overlooking the yard so make my presence known and watch them and my husband is in our garden adjoining the area at least once a day. There is a woods right beside the one side of the fence and the young stock wiggle under the fence and peck around in there. Where they are getting through is only about 2 inches from the ground and we have been trying to plug it and are exhausted from chasing them back in - they just turn around when we are in the house and go back. I'm sure whatever is picking them off just lays in wait there. We were wondering if putting up a 6ft. fence and burying the bottom into the ground would help? Or would a coyote or fox simply jump the fence and run off with them? We have found only one carcass - some feathers and a few picked bones. In my young stock I had 4 roosters and 6 hens and I was hoping to incubate their eggs later on for more chicks. I was going to keep 2 roosters and put two in the freezer - now I'm down to ONE ROOSTER. I panicked and so moved the 6 hens and l rooster into a smaller henhouse with no access to outside. I feel badly they can't free range but I can afford to lose any of them. I have l0 brown sex hybrids raised from chicks this Spring that are with my older hens and not a one of them are missing. Its a very odd circumstance. The ducks and geese won't go in the henhouse at night and you'd think a fox or coyote would zero in on one of them but they haven't. Would an electric fence be better than a new 6 ft. welded wire fence? What do you all think? I'm flabbergasted at this point and don't want to have hens if I can't protect them - this is frustrating!!!. By the way we have no stray dogs and we own one old Westie who confines herself to the house so she is definitely not the problem. We have 4 housecats although three of them bring in mice and birds, all seem scared of the hens. Any thoughts?