From Hatchery mod.

Possible solutions:

• add support for addon developers to add custom resources
• move mature from Hatchery to Chickens
• item drop event?

not sure if it could work, but in hatchery the nesting pens,
I turn on the "entity.captureDrops" = true,
and than removing them from the items from the entity and transfer them to the nesting pen with the
"entityCapturedDrops" array.

I'm using the proper entity dropItem method.

So I looked and your checking for a henhouse on the entity update method.
So what you could use the boolen method if a hen house is nearby. If it is than turn on capture items.
Than drop the item and after that check if captured items has items in it..
and than place them all into the hen house.

If you have dont anything with this yet.. I can make a pr for you to look at. it will look beter than my ladt one. I wont do it on my phone.