Some cleanup of the Birkhoff transcription and tests. #1877

Job	Run time
test_ubuntu (baseline, 3.12, 1.26, 1.13, 3.21.0, v2.11.0, 7.7, latest, true, [all], 0.4.28, false)	1h 5m 28s
test_ubuntu (no_pyoptsparse, 3.12, 1.26, 1.13, 3.21.0, latest, [test], false)	15m 16s
test_ubuntu (numpy2_no_pyoptsparse, 3.12, 2, 1.14, latest, [all], false)	16m 38s
test_ubuntu (no_snopt, 3.12, 1.26, 1.13, 3.21.0, v2.11.0, latest, [all], 0.4.28, false)	1h 6m 22s
test_ubuntu (no_mpi, 3.12, 1.26, 1.13, v2.11.0, latest, [test], false)	53m 45s
test_ubuntu (latest, 3.12, 1, 1, 3.21.0, latest, 7.7, dev, [all], latest, false)	53m 6s
test_ubuntu (python313, 3.13, 2, 1, 3.22.2, 7.7, dev, [test], latest, false)	15m 42s
test_ubuntu (oldest, 3.9, 1.22, 1.7, 4.0, 3.0, 3.13, v2.9.0, 7.2, 3.28.0, 3.5, [test], false)	39m 50s
Finish coveralls	0s
	5h 26m 7s

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