To make glaze, bring juice and rum to a simmer and simmer until reduced by half. Add the vinegar, corn syrup, Worcestershire, cane syrup, tomato paste and stock and simmer until reduced by one quarter. Combine cornstarch with a splash of water until smooth and whisk into glaze. Simmer 10 more minutes. Off heat, stir in zest
To prepare hens, rinse inside and out and dry well with paper towels. Salt and pepper inside and out, insert 1/4 Satsuma, tangerine or orange and sprig of herbs into cavity, and truss legs together with kitchen twine if desired. Cover wing tips with foil.
Glaze hens and cook in preheated 400 degree oven for 20 minutes. Reglaze and return to oven for another 15 minutes. Glaze again, and tent loosely with foil if skins are browning too fast; return to oven for 45 minutes.
Check thickest part of breast with a meat thermometer; if not up to 170 degrees, glaze again and return to oven for 10 minutes at a time until temperature reached. Let rest for 10 minutes before serving.