^^^ THIS ^^^
If you are tilling pine shavings down into the soil profile, they will tie up N, even with the extensive N you're adding with the manure.
I'd consider composting those shavings and chicken poo with a mix of other bio-mass, and then apply the finished (or semi-finished)
compost as a top-dressing.
Consider also going toward a no-till approach. In order for this to work, a layer of
mulch over the entire surface is the best way to keep weeds down and retain moisture and soil fertility. Spoiled
hay,
wood chips, or any one of a number of other mulches are commonly used in gardens. (I'm a HUGE fan of wood chips and use them extensively --- the so-called "Back to Eden" method.) If you were to use such a no-till/heavy mulch method, you can just top dress with your uncomposted pine shavings and chicken poo. The nutrients will make their way down into the soil with every rain.
Perhaps experiment a bit this year. Mulch in one area, till in another, go no-till in a third area with varying levels of mulch . . . mess around a bit and see what happens.
One last thought: it sounds like the lack sunlight and presence of cool air may be part of your issue. Can you open the neighboring trees up a bit so that more light makes it though to your garden? Take out limbs or even selectively thin the forest a bit so afternoon sun can make it through. More than just blocking the sunlight from reaching your plants, those trees will create a micro-climate that is much cooler. It takes much longer to warm up in the morning, and it will get much cooler later in the afternoon. Most garden plants like warm nights and quickly warmed soil in the morning. Your micro-climate may be continually cool, as a mass of cool air is held by those trees late into the morning. That cold air settles over your garden for 6 hours or perhaps more, until the sun is directly overhead and it warms up.
Have you ever taken a walk and noticed how much cooler it gets when you descend into a ravine or little valley? It'll drop 15 degrees in a matter of a hundred steps. Have you ever ridden on a motor cycle and driven past fields, stands of trees, up and down vales and glens? You totally notice the temperature change. Its significant. The difference between 60 degrees and 75 is huge. The difference between 12 hours of sunlight and 8, again, is huge. The difference between a microclimate where heat is stored in, for example, a block wall, and a micro-climate where cool air moves down a slope over the top of your garden, clearly makes a difference with how those plants grow throughout the night. My warm loving plants (
tomatoes, almonds, peppers, citrus trees) are all planted on the west or south side of walls or other large structures that hold the heat into the evening. Other sun loving trees were planted on the east side of the swimming pool, because that late afternoon sun bounces off the pool and is caught by the trees. I've got apricot and aprium trees that continually lean toward the pool to get every possible available photon.
Anyhow, there may not be just one variable here (nitrogen), but several.
Best of luck with your garden this season. Mess around, make mistakes, and see what works better.