Hello Lucy, 

Thanks for reaching out to UVM Extension Master Gardener Helpline.

Before taking any action (neem, pruning, etc), I would confirm what you're dealing with.

First, I would confirm if that white substance is indeed a sap. I don't have a ton of experience with it but found a few resources that point to a fungal disease, Cytospora or Leucostoma canker, that is common with the spruce family. Inspect the tree from top to bottom to see if there are any other indications of white sap or die-back/needle drop. Check out these resources for more info on diagnosing and potential corrective actions: 

https://extension.umd.edu/resource/cytospora-canker-spruce-trees/

https://hort.extension.wisc.edu/articles/cytospora-canker-2/#:~:text=Cytospora%20canker%20is%20caused%20by,%2C%20insects%2C%20birds%20and%20mammals.

It's hard to tell from the photos, but you should also closely inspect the die-back area for holes in the tree. That might indicate a borer or weevil of some sort. Check these resources for more info on White Pine weevil and others spruce issues: 

https://bygl.osu.edu/index.php/node/826

https://files.dnr.state.mn.us/assistance/backyard/treecare/forest_health/whitesprucediagnosis.pdf

Last, you might also consult a certified arborist to assess the trees. Go to www.treesaregood.org, the website of the International Society of Arboriculture.

Hope that helps. If you have other questions, please reach out.