Q.Crape Myrtle Issue
Our crepe myrtle (at least 15 years old) grew many little spikes on the trunk over the past month or so. They look like 4-inch-long pieces of angel hair pasta, sticking out all over the main trunk. Now, the branches are dying in chunks. Any idea what the problem might be? I’m not finding a match with typical myrtle tree diseases/issues.

From your description is sounds like spindle galls, which are caused by an infestation of pests; it could be any number of pests.
Do further inspection of the tree and look for any other signs of pest or disease.
These links will help you pinpoint the issue.
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-tree-problems.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-bark-scale.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/yellowing-crepe-myrtle-leaves.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-tip-blight.htm
https://www.extension.umn.edu/garden/insects/find/insect-and-mite-galls/
https://www.clemson.edu/extension/hgic/pests/pdf/hgic2002.pdf