"There are squirrels but it is hard to imagine that they eat everyone in 2-5 days "
LOL. Really? I find it easy to imagine and have seen it. Also, birds, specially crow, will flock in and strip fruit trees all within a few minutes.
I see you have St.Augustine grass so the mulberry is getting plenty of water. Maybe that is what is causing it low fruit production??? My tree gets zero water and it produces great.
I did have a Thai everbearing that never got fertilizer or water and overproduced. It was eventually taking out by a neighbor due to it was on a shared easement. But, good riddance as it dropped fruit on the pavement and stained it unsightly. Now I just have the Tice variety and it also never gets watered and fertilized and it produces a lot. However...you have to pick them daily when they turn black otherwise birds/squirrels will take them.
To me, and I'm definitely no expert, but IMHO, mulberry needs no care to produce fruit.
also, tonight I'm going to cover my jaboticaba with foil. I did a forum search and didn't see any photos. But, I'm just going to wrap the whole limb and fruit with foil.