Some cleanup of the Birkhoff transcription and tests. #1894

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 6m 33s
test_ubuntu (no_pyoptsparse, 3.12, 1.26, 1.13, 3.21.0, latest, [test], false)	15m 52s
test_ubuntu (numpy2_no_pyoptsparse, 3.12, 2, 1.14, latest, [all], false)	17m 8s
test_ubuntu (no_snopt, 3.12, 1.26, 1.13, 3.21.0, v2.11.0, latest, [all], 0.4.28, false)	1h 5m 24s
test_ubuntu (no_mpi, 3.12, 1.26, 1.13, v2.11.0, latest, [test], false)	55m 0s
test_ubuntu (latest, 3.12, 1, 1, 3.21.0, latest, 7.7, dev, [all], latest, false)	55m 37s
test_ubuntu (python313, 3.13, 2, 1, 3.22.2, 7.7, dev, [test], latest, false)	16m 7s
test_ubuntu (oldest, 3.9, 1.25, 1.9, 4.0, 3.0, 3.13, v2.10.2, 7.2, 3.36.0, 3.5, [test], false)	53m 44s
Finish coveralls	2s
	5h 45m 27s

Provide feedback