Can you contact the manufacture about the plastic type? I suspect its not acrylic, but more likely something like ABS or vinyl (PVC). Weld-on should still work in tis case, and would be better than superglue. I would start with the thin stuff wicked in from the backside, that will minimize the appearance from the front.
If there is a structural or ageing issue causing the cracks, the fix will only be temporary without reinforcing or other measures. Or were the cracks caused by impact?
If there is a structural or ageing issue causing the cracks, the fix will only be temporary without reinforcing or other measures. Or were the cracks caused by impact?