Fix facility discovery in exported builds and verify first construction

Makefile

@@ -111,6 +111,7 @@ check:
 export-windows:
 	mkdir -p build/windows
 	$(GODOT) --headless --path . --export-release "Windows Desktop"
+	$(MAKE) test-exported-opening
 
 # Pixel cutaway: interactive disposable inn, capture and input regression.
 .PHONY: preview-pixel capture-pixel test-pixel-ui
@@ -187,3 +188,9 @@ test-stairs:
 test-transport-comparison:
 	$(GODOT) --headless --path . --script res://tests/transport/test_transport_comparison.gd
 	$(GODOT) --headless --path . --script res://tests/transport/test_runtime_transport_comparison.gd
+
+# Check the actual shipped data outside this checkout, including first build.
+WINDOWS_PCK ?= build/windows/TheTree.pck
+.PHONY: test-exported-opening
+test-exported-opening:
+	python3 tools/verify_exported_opening.py "$(WINDOWS_PCK)" --godot "$(GODOT)"