I found these two papers on Medline. They focus on amount of epinephrine during/after labour, but neither found a link between epinephrine and labour length. Doesn't help much for answering questions about stress and going into labour though. Also not very large samples.
Schneider, H., Prögler, M., Ziegler, W. H., & Huch, R. (1990). Biochemical changes in the mother and the fetus during labor and its significance for the management of the second stage. International Journal of Gynecology & Obstetrics, 31(2), 117-126.
In 69 patients with uneventful pregnancies, term labor was studied prospectively with respect to length of second stage, number of bearing down efforts, maternal and fetal levels of lactate, epinephrine and norepinephrine. Maternal venous blood concentrations were measured in early labor and at the time of delivery while samples from umbilical artery and vein provided fetal blood. There was a significant rise of lactate and catecholamines in maternal blood during labor and at delivery fetal lactate concentration was lower than the maternal level while for epinephrine and norepinephrine fetal levels were higher. For all three compounds umbilical artery concentrations were higher than umbilical venous levels. While there was no correlation between the biochemical parameters in maternal blood and length of second stage maternal lactate and norepinephrine concentration at the time of delivery significantly correlated with the number of bearing down efforts. Umbilical artery lactate correlated with both, length of second stage and number of bearing down efforts.
Okutomi, T., Mochizuki, J., Amano, K., & Hoka, S. (2000). Effect of epidural epinephrine infusion with bupivacaine on labor pain and mother-fetus outcome in humans. Regional anesthesia and pain medicine, 25(3), 228-234.
BACKGROUND AND OBJECTIVES: Epinephrine is used with local anesthetics to prolong the duration of epidural analgesia and decrease the peak plasma concentrations of local anesthetics. In the practice of obstetric anesthesia, the utero-placental and fetal effects of epinephrine are controversial issues. We designed a prospective, randomized, and double-blind study to examine the effects of epinephrine infusion on the quality of analgesia and uterine or umbilical blood flows with Doppler ultrasound, as well as the duration of the first or the second stage of labor, and fetal outcome. METHODS: Twenty-eight parturients received continuous epidural bupivacaine 0.25% (4 mL/h) combined either with epinephrine (20 microg/h) (n = 13) or without epinephrine (n = 15) for analgesia during labor. If patients requested additional analgesia, an additional bolus of 1% or 1.5% lidocaine (6 to 10 mL) was administered. RESULTS: The total amount of additional lidocaine was greater in the plain bupivacaine group (130 [0, 280] mg; median [25th, 75th percentile] with P < .05) than in the epinephrine group (0 [0, 60] mg). Epinephrine infusion did not alter the resistance of the uterine and umbilical arteries as measured by resistance index. The duration of the first or second stages of labor did not significantly differ in the 2 groups. Epinephrine infusion did not change the fetal heart rate or the blood gas data in the umbilical artery. CONCLUSIONS: A low-dose epidural infusion of epinephrine decreased anesthetic requirements.