After much hair pulling and trying this and that and searching all over and taking bits of code from here and there, I managed to patch together something that does what I was hoping for.
#animation sequence duplication script by James Oliver, 2022_July_11
#Given a mesh with shape keys with keyframes and other animation keyframes,
#this script will output a series of shapes from frame frame-start to
#frame frame_end with shape keys and animation data stripped.
#The object must be selected.
import bpy
ctxt = bpy.context
selected_object_old = bpy.context.active_object
frame_start = 1
frame_end = 44
bpy.context.scene.frame_set(frame_start)
x = frame_start
while x <= frame_end:
deep = bpy.context.evaluated_depsgraph_get()
cleaned_copy = selected_object_old.copy()
cleaned_copy.data = selected_object_old.data.copy()
cleaned_copy.animation_data_clear()
ctxt.collection.objects.link(cleaned_copy)
evaluated_object = selected_object_old.evaluated_get(deep)
clean_mesh = bpy.data.meshes.new_from_object(evaluated_object)
cleaned_copy.data = clean_mesh
x += 1
bpy.context.scene.frame_set(x)